BA-54: Real Estate Programs
Background: The Texas Instruments BA-54 is a 1986 update of the BA-55 (not a typo) financial calculator. The BA-54 is a keystroke programming calculator which can hold up to 40 programming steps. However, it’s up to 40 programming steps or up to 5 memory registers (register 1 through 5). Programming mode only occurs in finance mode, though the BA-54 also has a cash flow mode and a statistics (linear regression) mode.
Because steps can add up quickly, limited memory registers are really available. Going beyond step 32 will leave no memory register to work with.
My review of the BA-55 from 2018: http://edspi31415.blogspot.com/2018/02/retro-review-texas-instruments-ba-55.html
APR (Annual Percentage Rate) with Fees
Inputs:
number of payments [ N ]
annual interest rate ÷ 12 = [ %i ]
gross loan amount [ PV ]
points (in %) [ STO ] 1
Operation:
[ 2nd ] (RST) [ R/S ] payment of the loan (PMT, shown as a positive number)
[ R/S ] APR of the rate when fees are considered
APR is based off the net loan amount (gross loan amount – points%)
Code:
KEY |
STEP # |
KEY CODE |
CPT |
00 |
12 |
PMT |
01 |
23 |
R/S |
02 |
13 |
1 |
03 |
01 |
- |
04 |
75 |
RCL |
05 |
71 |
1 |
06 |
01 |
% |
07 |
52 |
= |
08 |
95 |
× |
09 |
65 |
RCL |
10 |
71 |
PV |
11 |
24 |
= |
12 |
95 |
PV |
13 |
24 |
CPT |
14 |
12 |
%i |
15 |
22 |
× |
16 |
65 |
1 |
17 |
01 |
2 |
18 |
02 |
= |
19 |
95 |
R/S |
20 |
13 |
RST |
21 |
37 |
Example
What is true APR on a 20 year loan when the loan amount is 58000 at 6.8% when the loan carries the cost of 3.5 points?
Inputs:
20 [ × ] 12 [ = ] [ N ]
6.8 [ ÷ ] 12 [ = ] [ %i ]
58000 [ PV ]
3.5 [ STO ] 1 (points)
Operation:
[ 2nd ] (RST) [ R/S ] 442.74 (payment)
[ R/S ] 7.26% (APR with points)
The true APR is 7.26%.
Source
Smith, Jon M. Financial Analysis & Business Decisions on the Pocket Calculator. John Wiley & Sons: New York. 1976. pp. 177-178. ISBN 0-471-80184-4
Time and Interest Saved by Paying off a Loan Early
Inputs:
number of payments [ N ]
annual interest rate ÷ 12 = [ %i ]
gross loan amount [ PV ]
points (in %) [ STO ] 1
Operation:
Compute the payment by pressing [ PMT ]. Press [ 2nd ] (RST) [ R/S ].
Result: estimated original interest paid
Enter the new payment [ R/S ]
Result: number of payments with the higher payment [ R/S ]
Result: estimated interest saved
It is assumed that there are no penalties for early payment.
Code:
KEY |
STEP # |
KEY CODE |
RCL |
00 |
71 |
PMT |
01 |
23 |
× |
02 |
65 |
RCL |
03 |
71 |
N |
04 |
21 |
- |
05 |
75 |
RCL |
06 |
71 |
PV |
07 |
24 |
= |
08 |
95 |
STO |
09 |
61 |
1 |
10 |
01 |
R/S |
11 |
13 |
PMT |
12 |
23 |
CPT |
13 |
12 |
N |
14 |
21 |
R/S |
15 |
13 |
× |
16 |
65 |
RCL |
17 |
71 |
PMT |
18 |
23 |
- |
19 |
75 |
RCL |
20 |
71 |
PV |
21 |
24 |
= |
22 |
95 |
+/- |
23 |
94 |
SUM |
24 |
81 |
1 |
25 |
01 |
RCL |
26 |
71 |
1 |
27 |
01 |
R/S |
28 |
13 |
RST |
29 |
37 |
Example
We have a 30-year loan (360 payments) of 176000. The interest rate is 9.6%. If the user pays 1500 a month, how much time and interest are saved?
Inputs:
360 [ N ]
8 ÷ 12 = [ %i ]
176000 [ PV ]
Operation:
[ PMT ] Result: 1291.42
[ R/S ] Total original interest paid: 288913.24
Enter 1500 [ R/S ]
Result: 229.40 (n ≈ 230 payments) [ R/S ]
Result: 120808.27 (interest saved)
By paying 1500 instead of 1291.42, the loan will be paid about 230 payments (19 years, 2 months). Interest saved will be 120808.27.
The Front End Qualification Test
A common method to test whether a potential buyer of a house qualifies is the 28/36 Rule. Simply:
28% of the buyer’s monthly gross income is the maximum amount that the payment with their mortgage with insurance and property taxes (PITI) can be.
36% of the buyer’s monthly gross income is the maximum amount that PITI plus regular monthly debts can be.
The 28% is referred to as the front end test, while the 36% is referred to as the back end test.
The program returns two results: the PITI and difference between 28% of the gross income and PITI. If the difference is positive, the buyer pass the 28% test.
Due to the structure of how memory is set up, I could only fit the front end while being allowed to use 1 additional memory register.
Inputs:
number of payments [ N ]
annual interest rate ÷ 12 = [ %i ]
gross loan amount [ PV ]
monthly tax and property insurance [ STO ] 1
monthly gross income [ STO ] 2
Operation:
Compute the payment by pressing [ PMT ]. Press [ 2nd ] (RST) [ R/S ].
Result: PITI. (principal, interest, taxes, interest).
Press [ R/S ].
Result: Difference between 28% of income minus PITI.
KEY |
STEP # |
KEY CODE |
CPT |
00 |
12 |
PMT |
01 |
23 |
+ |
02 |
85 |
RCL |
03 |
71 |
1 |
04 |
01 |
= |
05 |
95 |
R/S |
06 |
13 |
RCL |
07 |
71 |
2 |
08 |
02 |
× |
09 |
65 |
2 |
10 |
02 |
8 |
11 |
08 |
% |
12 |
52 |
- |
13 |
75 |
RCL |
14 |
71 |
1 |
15 |
01 |
- |
16 |
75 |
RCL |
17 |
71 |
PMT |
18 |
23 |
= |
19 |
95 |
R/S |
20 |
13 |
RST |
21 |
37 |
Example
A potential buyer wants to finance a house with a 30 year term at 5%. The purchase price of 375000. The estimated monthly property and insurance is 250. The buyer earns a monthly income of 12000. Does the buyer qualify (at least pass the front test (28%))?
Inputs:
30 [ × ] 12 [ = ] [ N ]
5 ÷ 12 = [ %i ]
375000 [ PV ]
250 [ STO ] 1
12000 [ STO ] 2
Operation:
Compute the payment by pressing [ PMT ]. Press [ 2nd ] (RST) [ R/S ].
Result: 2263.08 (principal, interest, taxes, interest).
Press [ R/S ].
Result: 1096.92 (it is positive, so the buyer passes the 28% test)
Source
Probasco, Jim. “What is the 28/36 rule for home affordability?” Bankrate. 09 October 2023, https://www.bankrate.com/real-estate/what-is-the-28-36-rule/ Retrieved October 16, 2024.
Enjoy!
Eddie
All original content copyright, © 2011-2025. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.
