HP 12C User guide
Introduction
This Solutions Handbook has been designed to supplement the HP-12C Owner's
Handbook by providing a variety of applications in the financial area. Programs
and/or step-by-step keystroke procedures with corresponding examples in each
specific topic are explained. We hope that this book will serve as a reference
guide to many of your problems an d will show you how to redesign our examples
to fit your specific needs.
Real Estate
Refinancing
It can be mutually advantageous to both borrower and lender to refinance an
existing mortgage which has an interest rate substantially below the current
market rate, with a loan at a below-market rate. The borrower has the immediate
use of tax-free cash, while the lender has substantially increased debt service on
a relatively small cash outlay.
To find the benefits to both borrower and lender:
1. Calculate the monthly payment on the existing mortgage.
2. Calculate the monthly payment on the new mortgage.
3. Calculate the net monthly payment received by the lender (and paid by the borrower) by
adding the figure found in Step 1 to the figure found in Step 2.
4. Calculate the Net Present Value (NPV) to the lender of the net cash advanced.
5. Calculate the yield to the lender as an IRR.
6. Calculate the NPV to the borrower of the net cash received.
Example 1: An investment property has an existing mortgage which originated 8
years ago with an original term of 25 years, fully amortized in level monthly
payments at 6.5% interest. The current balance is $133,190.
Although the going current market interest rate is 11.5%, the lender has agreed
to refinance the property with a $200,000, 17 year, level-monthly-payment loan at
9.5% interest.
What are the NPV and effective yield to the lender on the net abount of cash
actually advanced?
What is the NPV to the borrower on this amount if he can earn a 15.25% equity
yield rate on the net proceeds of the loan?
Keystrokes Display
CLEAR
17
6.5
-1,080.33
Monthly payment on existing mortgage received by
lender.
133190
0
9.5
200000
1,979.56 Monthly payment on new mortgage.
0
133190
11.5
0
0
12
15.25
0
0
899.23 Net monthly payment (to lender).
-66,810.00 Net amount of cash advanced (by lender).
-80,425.02 Present value of net
-13,615.02
14.83
-65,376.72 Present value of net monthly payment at 15.25%.
1,433.28
NPV to lender of net cash advanced
% nominal yield (IRR).
NPV to borrower.
Wrap-Around Mortgage
A wrap-around mortgage is essentially the same as a refinancing mortgage,
except that the new mortgage is granted by a different lender, who assumes the
payments on the existing mortgage, which remains in full force. The new
(second) mortgage is thus "wrapped around" the existing mortgage. The "wraparound" lender advances the net difference between the new (second) mortgage
and the existing mortgage in cash to the borrower, and receives as net cash flow,
the difference between debt service on the new (second) mortgage and debt
service on the existing mortgage.
When the terms of the origin al mortgage and the wrap-around are the same, the
procedures in calculating NPV and IRR to the lender and NPV to the borrower
are exactly the same as those presented in the preceding section on refinancing.
Example 1: A mortgage loan on an income property has a remaining balance of
$200,132.06. When the load originated 8 years ago, it had a 20-year term with
full amortization in level monthly payments at 6.75% interest.
A lender has agreed to "wrap" a $300,000 second mortgage at 10%, with full
amortization in level monthly payments over 12 years. What is the effective yield
(IRR) to the lender on the net cash advanced?
Keystrokes Display
144.00
Total number of months remaining in original load
(into n).
CLEAR
20
8
6.75
200132.06
10
300000
200132.06
12
0
0
0.56 Monthly interest rate (into i).
200,132.06 Loan amount (into PV).
-2,031.55 Monthly payment on existing mortgage (calculated).
0.83 Monthly interest on wrap-around.
-300,000.00 Amount of wrap-around (into PV).
3,585.23 Monthly payment on wrap-around (calculated).
1,553.69 Net monthly payment received (into PMT).
-99,867.94 Net cash advanced (into PV).
15.85
Nominal yield (IRR) to lender (calculated).
Sometimes the wrap around mortgage will have a longer payback period than the
original mortgage, or a balloon payment may exist.
where:
n1 = number of years remaining in original mortgage
PMT
= yearly payment of original m ortgage
1
= remaining balance of orig ina l m ort gage
PV
1
n
= number of years in wrap-around mortgage
2
PMT
= yearly payment of wrap-around m or tgage
2
PV
= total amount of wrap-around mortgage
2
BAL = balloon payment
Example 2: A customer has an existing mortgage with a balance of $125.010, a
remaining term of 200 months, and a $1051.61 monthly payment. He wishes to
obtain a $200,000, 9 1/2% wrap-around with 240 monthly payments of $1681.71
and a balloon payment at the end of the 240th month of $129,963.35. If you, as a
lender, accept the proposal, what is your rate of return?
Keystrokes Display
CLEAR
200000
125010
1051.61
1681.71
2
39
99
129963.35
-74,990.00 Net investment.
630.10 Net cash flow received by lender.
The above cash flow occurs 200 times.
1,681.71 Next cash flow received by lender.
39.00 Cash flow occurs 39 times.
131,645.06 Final cash flow.
12
11.84 Rate of return to lender.
If you, as a lender, know the yield on the entire transaction, and you wish to
obtain the payment amount on the wrap-around mortgage to achieve this yield,
use the following procedure. Once the monthly payment is known, the borrower's
periodic interest rate may also be determined.
1. Press the and press CLEAR .
2. Key in the remaining periods of the original mortgage and press
3. Key in the desired annual yield and press
4. Key in the monthly payment to be made by the lender on the original mortgage and press
.
5. Press
6. Key in the net amount of cash advanced and press
7. Key in the total term of the wrap-around mortgage and press
8. If a balloon payment exists, key it in and press
9. Press
10. Key in the amount of the wrap-around mortgage and press
borrower's periodic interest rate.
.
to obtain the payment amount necessary to achieve the desired yield.
.
.
.
.
.
to obtain the
Example 3: Your firm has determined that the yield on a wrap-around mortgage
should be 12% annually. In the previous example, what monthly payment must
be received to achieve this yield on a $200,000 wrap-around? What interest rate
is the borrower paying?
Keystrokes Display
CLEAR
200
1051.61
240
129963.35
12
74990
Number of periods and monthly interest rate.
-165,776.92 Present value of payments plus cash advanced.
1,693.97 Monthly payment received by lender
9.58 Annual interest rate paid by borrower.
12
Income Property Cash Flow Analysis
Before-Tax Cash Flows
The before-tax cash flows applicable to real estate analysis and problems are:
Potential Gross Income
•
Effective Gross Income
•
Net Operating Income (also called Net Income Before Recapture.)
•
Cash Throw-off to Equity (also called Gross Spendable Cash)
•
The derivation of these cash flows follows a set sequence:
1. Calculate Potential Gross Income by multiplying the rent per unit times the number of
units, times the number of rental payments periods per year. This gives the rental income
the property would generate if it were fully occupied.
2. Deduct Allowance for Vacancy and Rental Loss. This is usually expressed as a
percentage. The result is Rent Collections (which is also Effective Gross Income if there
is no "Other Income").
3. Add "Other Income" such as receipts from concessions (laundry equipment, etc.),
produced from sources other than the rental office space. This is Effective Gross Income.
4. Deduct Operating Expenses. These are expenditures the landlord-investor must make,
by contract or custom, to preserve the property and keep in capable of producing the
gross income. The result is the Net Operating Income.
5. Deduct Annual Debt Service on the mortgage. This produces Cash Throw-Off to Equity.
Thus:
Effective Gross Income =
Potential Gross Income - Vacancy Loss + Other Income.
Net Operating Income =
Effective Gross Income - Operating Expenses.
Cash Throw-Off =
Net Operating Income - Annual Dept Service.
Example: A 60-unit apartment building has rentals of $250 per unit per month.
With a 5% vacancy rate, the annual operating cost is $76,855.
The property has just been financed with a $700,000 mortgage, fully amortized in
a level monthly payments at 11.5% over 20 years.
a. What is he Effective Gross Income?
b. What is the Net Operating Income?
c. What is the Cash Throw-Off to Equity?
Keystrokes Display
CLEAR
60
250
5
76855
20
11.5
700000
12
12
180,000.00 Potential Gross Income.
9,000.00 Vacancy Loss.
171,000.00 Effective Gross Income.
94,145.00 Net Operating Income.
-89,580.09 Annual Debt Service.
4,564.91 Cash Throw-Off.
Before-Tax Reversions (Resale Proceeds)
The reversion receivable at the end of the income projection period is usually
based on forecast or anticipated resale of the property at that time. The beforetax reversion amount applicable to real estate analysis and problems are:
Sale Price.
•
Cash Proceeds of Resale.
•
Outstanding Mortgage Balance.
•
Net Cash Proceeds of Resale to Equity.
•
The derivation of these reversions are as follows:
1. Forecast or estimate Sales Price. Deduct sales and Transaction Costs. The result is the
Proceeds of Resale.
2. Calculate the Outstanding Balance of the Mortgage at the end of the Income Projection
Period and subtract it from Proceeds of Resale. The result is net Cash Proceeds of
Resale.
Thus:
Cash Proceeds of Resale =
Sales Price - Transaction Costs.
Net Cash Proceeds of Resale =
Cash Proceeds of Resale - Outstanding Mortgage Balance.
Example: The apartment property in the preceding example is expected to be
resold in 10 years. The anticipated resale price is $800,000. The transaction
costs are expected to be 7% of the resale price. The mortgage is the same as
that indicated in the preceding example.
What will the Mortgage Balance be in 10 years?
•
What are the Cash Proceeds of Resale and Net Cash Proceeds of Resale?
•
Keystrokes Display
CLEAR
240.00 Mortgage term.
20
11.5
700000
10
800000
7
0.96 Mortgage rate.
Property value.
-7,465.01 Monthly payment.
120.00 Projection period.
-530,956.57 Mortgage balance in 10 years.
Estimated resale.
56,000.00 Transaction costs.
744,000.00 Cash Proceeds of Resale.
213,043.43 Net Cash Proceeds of Resale.
After-Tax Cash Flows
The After-Tax Cash Flow (ATCF) is found for the each year by deducting the
Income Tax Liability for that year from the Cash Throw Off.
where:
Taxable Income =
Net Operating Income - interest - depreciation.
Tax Liability =
Taxable Income x Marginal Tax Rate.
After Tax Cash Flow =
Cash Throw Off - Tax Liability.
The After-Tax Cash Flow for the initial and successive years may be calculated
by the following HP-12C program. This program calculates the Net Operating
Income using the Potential Gross Income, operational cost and vacancy rate.
The Net Operating Income is readjusted each year from the growth rates in
Potential Gross Income and operational costs.
The user is able to change the method of finding the depreciation from declining
balance to straight line. To make the change, key in at line 32 of the
program in place of .
KEYSTROKES DISPLAY
CLEAR
0
1
7
2
7
1
1
1
2
0001- 0
02- 11
03- 44 1
04- 45 7
05- 26
06- 2
07- 10
08- 44 7
09- 1
10-44 40 1
11- 1
12- 2
0
5
6
6
4
13- 42 11
14- 44 0
15- 45 5
16- 11
17- 45 12
18- 45 6
19- 12
20- 33
21- 44 6
22- 33
23- 45 13
24- 45 4
25- 13
26- 33
4
27- 44 4
0
36
1
0
28- 33
29- 43 35
30-43,33 36
31- 45 1
32- 42 25
33-44 30 0
34- 0
17
2
8
2
35-43,33 17
36- 11
37- 45 2
38- 45 8
39- 25
40-44 40 2
1
0
3
9
3
41- 33
42-45 48 0
43- 25
44- 30
45- 45 3
46- 45 9
47- 25
48-44 40 3
49- 33
50- 30
51- 1
7
0
52- 45 7
53-44 20 0
54- 30
1
55- 20
56- 45 14
57- 1
2
0
1
09
REGISTERS
n: Used i: Annual %
PV: Used PMT: Monthly
FV: 0 R0: Used
R1: Counter
R3: Oper. cost R4: Dep. value
R5: Dep. life R6: Factor (DB)
R7: Tax Rate R8: % gr. (PGI)
R9: % gr. (op) R.0: Vacancy rt.
58- 2
59- 20
60- 40
61- 45 0
62- 30
63- 45 1
64- 43 31
65- 34
66- 31
67-43,33 09
R
: PGI
2
1. Press and press CLEAR .
2. Key in loan values:
Key in annual interest rate and press
•
Key in principal to be paid and press
•
Key in monthly payment and press
•
(If any of the values are not known, they should be solved for.)
3. Key in Potential Gross Income (PGI) and press
4. Key in Operational cost and press
3.
2.
5. Key in depreciable value and press 4.
6. Key in depreciable life and press
7. Key in factor (for declining balance only) and press
8. Key in the Marginal Tax Rate (as a percentage) and press
9. Key in the growth rate in Potential Gross Income ( 0 for no growth) and press
10. Key in the growth rate in operational cost (0 if no growth) and press
11. Key in the vacancy rate (0 for no vacancy rate) and press
12. Key in the desired depreciation function at line 32 in the program.
13. Press
with the ATCF for that year. The Y-register contains the year.
14. Continue pressing
to compute ATCF. The display will pause showing the year and then will stop
to compute successive After-Tax Cash Flows.
5.
6.
7.
8.
9.
0.
Example 1: A triplex was recently purchased for $100,000 with a 30-year loan at
12.25% and a 20% down payment. Not including a 5% annual vacancy rate, the
potential gross income is $9,900 with an annual growth rate of 6%. Operating
expenses are $3,291.75 with a 2.5% growth rate. The depreciable value is
$75,000 with a projected useful life of $20 years. Assuming a 125% declining
balance depreciation, what are the After-Tax Cash Flows for the first 10 years if
the investors Marginal Tax Rate is 35%?
Keystrokes Display
CLEAR
100000
20
12.25
30
9900 2
3291.75 3
75000 4
20 5
80,000.00 Mortgage amount.
1.02 Monthly interest rate.
360 Mortgage term.
-838.32 Monthly payment.
9,900.00 Potential Gross Income.
3,291.75 1st year operating cost.
75,000.00 Depreciable value.
20.00 Useful life.
125 6
125.00 Decline in balance factor.
35 7
6 8
2.5 9
5 .0
35.00 Marginal Tax Rate.
6.00 Potential Gross Income growth rate.
2.50 Operating cost growth.
5.00 Vacancy rate.
1.00
-1,020.88
2.00
-822.59
3.00
-598.85
4.00
-72.16
5.00
232.35
6.00
565.48
7.00
928.23
8.00
1,321.62
9.00
1,746.81
10.00
-1,020.88
Year 1
ATCF
1
Year 2
ATCF
2
Year 3
ATCF
3
Year 4
ATCF
4
Year 5
ATCF
5
Year 6
ATCF
6
Year 7
ATCF
7
Year 8
ATCF
8
Year 9
ATCF
9
Year 10
ATCF
10
Example 2: An office building was purchased for $1,400,000. The value of
depreciable improvements is $1,200,000.00 with a 35 year economic life.
Straight line depreciation will be used. The property is financed with a $1,050,000
loan. The terms of the loan are 9.5% interest and $9,173.81 monthly payments
for 25 years. The office building generates a Potential Gross Income of
$175,2000 which grows at a 3.5% annual rate. The operating cost is $40,296.00
with a 1.6% annual growth rate. Assuming a Marginal Tax Rate of 50% and a
vacancy rate of 7%, what are the After-Tax Cash Flows for the first 5 years?
Keystrokes Display
CLEAR
1050000
9173.81
175,200.00 Potential Gross Income.
25
175200
40296 3
1200000 4
35 5
50 7
3.5 8
1.6 9
7 0
2
31
40,296.00 1st year operating cost.
1,200,000.00 Depreciable value.
35.00 Depreciable life.
50.00 Marginal tax rate.
3.50 Potential Gross Income
1.60 Operating cost growth rate.
7.00 Vacancy rate.
7.00 Go to dep. step.
32- 42
23
1.00
18,021.07
2.00
20,014.26
3.00
22,048.90
4.00
24,123.14
5.00
26,234.69
Change to SL.
Year 1
ATCF
1
Year 2
ATCF
2
Year 3
ATCF
3
Year 4
ATCF
4
Year 5
ATCF
5
After-Tax Net Cash Proceeds of Resale
The After-Tax Net Cash Proceeds of Resale (ATNCPR) is the after-tax reversion
to equity; generally, the estimated resale price of the property less commissions,
outstanding debt and any tax claim.
The After-Tax Net Cash Proceeds can be found using the HP-12C program
which follows. In calculating the owner's income tax liability on resale, this
program assumes that the owner elects to have his capital gain taxed at 40% of
his Marginal Tax Rate. This assumption is in accordance with a 1978 Federal tax
ruling.
* (*
Federal Taxes, code sec. 1202 (32,036))
This program uses declining balance depreciation to find the amount of
depreciation from purchase to sal e. This amount is used to determine the excess
depreciation (which is equal to the amount of actual depreciation minus the
amount of the straight line depreciation).
The user may change to a different depreciation method by keying in the desired
function at line 35 in place of .
KEYSTROKES DISPLAY
CLEAR
2
4
1
0001- 43 8
02- 44 2
03- 33
04- 25
05- 30
06- 44 0
07- 30
08- 48
09- 4
10- 20
11- 44 1
12- 45 14
13- 42 14
14- 14
2
0
CLEAR
3
4
5
15- 45 2
16- 43 11
17- 15
18-44 40 0
19- 42 34
20- 45 3
21- 13
22- 45 4
23- 11
24- 45 5
25- 12
6
2
2
26- 45 2
27- 42 23
28- 45 2
29- 20
30- 48
31- 6
1
2
1
32- 20
33-44 40 1
34- 45 2
35- 42 25
36- 34
37- 45 13
38- 30
39-44 40 1
6
2
1
0
00
REGISTERS
n: Used i: Used
PV: Used PMT: Used
FV: Used R0: Used
R1: Used R2: Desired yr.
40- 45 6
41- 26
42- 2
43- 10
44- 45 1
45- 20
46- 45 0
47- 40
48-43,33 00
R3: Dep. value R4: Dep. life
R5: Factor R6: MTR
R7-R.3: Unused
1. Key in the program and press CLEAR .
2. Key in the loan values:
Key in annual interest rate and press
•
Key in mortgage amount and press
•
Key in monthly payment and press
•
(If any of the values are unknown, they should be solved for.)
3. Key in depreciable value and press
4. Key in depreciable life in years and press
5. Key in accelerated depreciation factor for the declining balance method and press
5.
6. Key in your Marginal Tax Rate as a percentage and press
7. Key in the purchase price and press
8. Key in the sale price and press
9. Key in the % commission charged on the sale and press
*
If a dollar value is desired instead of a commission rate, key in , which does
3.
4.
.
.
.
.
.
6.
.*
not affect the register values, at line 04 of the program.
10. Key in the number of years after purchase and press
.
Example 1: An apartment complex, purchased for $900,000 ten years ago, is
sold for $1,750,000. The closing cost are 8% of the sale price and the income tax
rate is 48%.
A $700,000 loan for 20 years at 9.5% annual interest was used to purchase the
complex. When it was purchased the depreciable value was $750,000 with a
useful life of 25 years. Using 125% declining balance depreciation, what are the
After-Tax Net Cash Proceeds in year 10?
Keystrokes Display
CLEAR
0.00
700000
700,000.00 Mortgage.
9.5
20
750000 3
25 4
125 5
48 6
900000
1750000
8
10
0.79 Monthly interest.
240.00 Number of payments.
-6,524.92 Monthly payment.
750,000.00 Depreci abl e value.
25.00 Depreciable life.
125.00 Factor.
48.00 Marginal Tax Rate.
900,000.00 Purchas e pr ice.
1,750,000.00 Sale price.
8.00 Commission rate.
911,372.04
ATNCPR.
Lending
Loan With a Constant Amount Paid Towards Principal
This type of loan is structured such that the principal is repaid in equal
installments with the interest paid in addition. Therefor each periodic payment
has a constant amount applied toward the principle and a varying amount of
interest.
Loan Reduction Schedule
If the constant periodic payment to principal, annual interest rate, and loan
amount are known, the total payment, interest portion of each payment, and
remaining balance after each successive payment may be calculated as follows:
1. Key in the constant periodic payment to principal and press 0.
2. Key in periodic interest rate and press
3. Key in the loan amount. If you wish to skip to another time period, press
key in the number of payments to be skipped, and press
4. Press
5. Press
6. Press
7. Return to step 4 for each successive payment.
to obtain the interest portion of the payment.
0 to obtain the total payment.
0 to obtain the remaining balance of the loan.
.
. Then
0 .
Example 1: A $60,000 land loan at 10% interest calls for equal semi-annual
principal payments over a 6-year maturity. What is the loan reduction schedule
for the first year? (Constant payment to principal is $5000 semi-annually). What
is the fourth year's schedule (skip 4 payments)?
Keystrokes Display
5000 0
10
2
5.00 Semi-annual interest rate.
60000
0
3,000.00 First payment's interest.
8,000.00 Total first payment.
0
55,000.00 Remaining balance.
0
0
4 0
0
0
0
0
2,750.00 Second payment's interest.
7,750.00 Total second payment.
50,000.00 Remaining balance after the first year.
1,500.00 Seventh payment's interest.
6,500.00 Total seventh payment.
25,000.00 Remaining balance.
1,250.00 Eighth payment's interest.
6,250.00 Total eighth payment.
20,000.00 Remaining balance after fourth year.
Add-On Interest Rate Converted to APR
An add-on interest rate determines what po rtion of the principal will be added on
for repayment of a loan. This sum is then divided by the number of months in a
loan to determine the monthly payment. For example, a 10% add-on rate for 36
months on $3000 means add one-tenth of $3000 for 3 years (300 x 3) - usually
called the "finance charge" - for a total of $3900. The monthly payment is
$3900/36.
This keystroke procedure converts an add-on interest rate to a annual
percentage rate when the add-on rate and number of months are known.
1. Press and press CLEAR .
2. Key in the number of months in loan and press
3. Key in the add-on rate and press
4. Key in the amount of the loan and press
cash paid out.)
5. Press
6. Press
12 to obtain the APR.
.
.
.
* (*
Positive for cash received; negative for
.
Example 1: Calculate the APR and monthly payment of a 12% $1000 add-on
loan which has a life of 18 months.
Keystrokes Display
CLEAR
18
12
1,180.00 Amount of loan.
1000
12
-65.56 Monthly payment.
21.64 Annual Percentage Rate.
APR Converted to Add-On Interest Rate.
Given the number of months and annual percentage rate, this procedure
calculates the corresponding add-on interest rate.
1. Press and press CLEAR .
2. Enter the following information:
a. Key in number of months of loan and press
b. Key in APR and press
c. Key in 100 and press
3. Press
.
.
12 to obtain the add-on rate.
.
Example 1: What is the equivalent add-on rate for an 18 month loan with an
APR of 14%.
Keystrokes Display
CLEAR
14
18
100
12
7.63 Add-On Interes t Rate .
Add-On Rate Loan with Credit Life.
This HP-12C program calculates the monthly payment amount, credit life amount
(an optional insurance which cancels any remaining indebtedness at the death of
the borrower), total finance charge, and annual percentage rate (APR) for an
add-on interest rate (AIR) loan. The monthly payment is rounded (in normal
manner) to the nearest cent. If other rounding techniques are used, slightly
different results may occur.
KEYSTROKES DISPLAY
CLEAR
1
0
1
2
0
0
4
2
0001- 43 8
02- 1
03- 45 0
04- 1
05- 2
06- 0
07- 0
08- 10
09- 44 4
10- 45 2
11- 20
12- 30
13- 43 36
1
4
4
1
14- 45 1
15- 20
16- 45 4
17- 20
18- 30
19- 45 4
20- 45 1
21- 20
1
22- 1
3
0
0
23- 40
24- 34
25- 10
26- 45 3
27- 20
28- 45 0
29- 10
30- 42 14
31- 16
32- 14
33- 31
34- 45 14
35- 45 0
36- 20
37- 16
38- 13
39- 45 13
1
2
2
2
0
40- 45 2
41- 25
42- 45 0
43- 20
44- 1
45- 2
5
46- 10
47- 44 5
48- 26
49- 2
50- 20
51- 43 35
52- 43 35
0
1
61
5
53-43,33 61
54- 45 5
55- 48
56- 0
57- 1
5
5
3
58- 40
59- 42 14
60- 44 5
61- 45 5
62- 31
63- 45 13
64- 34
65- 30
66- 45 3
5
3
0
00
67- 30
68- 16
69- 31
70- 45 5
71- 45 3
72- 40
73- 13
74- 45 0
75- 11
76- 12
77-45,43 12
78-43,33 00
n: N i: i
PV: Used
FV: 0
R1: AIR R
R3: Loan
R5: Used R6-R9: Unused
1. Key in the program.
REGISTERS
PMT: PMT
: N
R
0
: CL (%)
2
R
: N/1200
4
2. Press
3. Key in the number of monthly payments in the loan and press
4. Key in the annual add-on interest rate as a percentage and press
5. Key in the credit life as a percentage and press
6. Key in the loan amount and press
7. Press
8. Press
9. Press
10. Press
CLEAR .
0.
1.
2.
3.
to find the monthly payment amount.
to obtain the amount of credit life.
to calculate the total finance charge.
to calculate the annual percentage rate.
11. For a new loan return to step 3.
Example 1: You wish to quote a loan on a $3100 balance, payable over 36
months at an add-on rate of 6.75%. Credit life (CL) is 1%. What are the monthly
payment amount, credit life amount, total finance charge, and APR?
Keystrokes Display
CLEAR
36
0
6.75 1
1 2
3100 3
36.00 Months.
6.75 Add-on interest rate.
1.00 Credit life (%).
3100.00 Loan.
-107.42 Monthly payment.
116.02 Credit life.
-651.10 Total finance charge.
12.39
APR.
Interest Rebate - Rule of 78's
This procedure finds the unearned interest rebate, as well as the remaining
principal balance due for a prepaid consumer loan using the Rule of 78's. The
known values are the current installment number, the total number of
installments for which the loan was written, and the total finance charge (amount
of interest). The information is entered as fol l ows:
1. Key in number of months in the loan and press 1.
2. Key in payment number when prepayment occurs and press
3. Key in total finance charge and press
to obtain the unearned interest (rebate).
4. Key in periodic payment amount and press
principal outstanding.
1 1 2
2 to obtain the amount of
2 1 .
Example 1: A 30 month $1000 loan having a finance charge of $180, is being
repaid at $39.33 per month. What is the rebate and balance due after the 25th
regular payment?
Keystrokes Display
30 1
25
1
180
2
5.81 Rebate.
1
1
2
39.33 2
190.84 Outstanding principal.
The following HP-12C program can be used to evaluate the previous example.
KEYSTROKES DISPLAY
CLEAR
00-
0
01- 44 0
1
2
1
2
2
02- 33
03- 44 2
04- 33
05- 44 1
06- 45 2
07- 30
08- 44 2
09- 1
0
1
10- 40
11- 45 0
12- 20
13- 45 1
14- 36
15- 20
1
2
2
00
REGISTERS
n: Unused i: Unused
16- 45 1
17- 40
18- 10
19- 45 2
20- 20
21- 31
22- 45 2
23- 20
24- 34
25- 30
26-43,33 00
PV: Unused PMT: Unused
FV: Unused R0: Fin. charge
R1: Payment # R2: # months
R3-R.6: Unused
1. Key in the program.
2. Key in the number of months in the loan and press
3. Key in the payment number when prepayment occurs and press
4. Key in the total finance charge and press
5. Key in the periodic payment amount and press
outstanding.
6. For a new case return to step 2.
Keystrokes Display
30
25
180
39.33
5.81 Rebate.
190.84 Outstanding balance.
to obtain the unearned interest (rebate).
to find the amount of principal
Graduated Payment Mortgages
.
.
The Graduated Payment Mortgage is designed to meet the needs of young home
buyers who currently cannot afford high mortgage payments, but who have the
potential of increasing earning in the years on come.
Under the Graduated Payment Mortgage plan, the payments increase by a fixed
percentage at the end of each year for a specified number of years. Thereafter,
the payment amount remains constant for remaining life of the mortgage.
The result is that the borrower pays a reduced payment (a payment which is less
than a traditional mortgage payment) in the early years, and in the later years
makes larger payments than he would with a traditional loan. Over the entire
term of the mortgage, the borrower would pay more than he would with
conventional financing.
Given the term of the mortgage (in years), the annual percentage rate, the loan
amount, the percentage that the payments increase, and the number of years
that the payments increase, the following HP-12C program determines the
monthly payments and remaining balance for each year until the level payment is
reached.
Loading...