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CH 10] Calculating Business 10-15

Loan Amortization Schedule

Loan Amount $400,000.00 Scheduled Payment $2,147.29
Annual Interest Rate 5.00% Scheduled number of payments 360
Loan period in years 30
Number of payments per year 12 Total Interest $373,023.14

Lender name: Bank of America 10

Pmt Beginning Total Ending Cumulative
No. Balance Payment Principal Interest Balance Interest
1 $ 400,000.00 $ 2,147.29 $ 480.62 $ 1,666.67 $399,519.38 $ 1,666.67
2 399,519.38 2,147.29 482.62 1,664.66 399,036.76 3,331.33
3 399,036.76 2,147.29 484.63 1,662.65 398,552.12 4,993.98
4 398,552.12 2,147.29 486.65 1,660.63 398,065.47 6,654.62
5 398,065.47 2,147.29 488.68 1,658.61 397,576.79 8,313.22
6 397,576.79 2,147.29 490.72 1,656.57 397,086.07 9,969.79
7 397,086.07 2,147.29 492.76 1,654.53 396,593.31 11,624.31
8 396,593.31 2,147.29 494.81 1,652.47 396.098.50 13,276.79
9 396,098.50 2,147.29 496.88 1,650.41 395,601.62 14,927.20
10 395,601.62 2,147.29 498.95 1,648.34 395,102.68 16,575.54
11 395,102.68 2,147.29 501.03 1,646.26 394.601.65 18,221.80
12 394,601.65 2,147.29 503.11 1,644.17 394,098.54 19,865.98

193 259,061.69 2,147.29 1,067.86 1,079.42 257,993.83 272,420.12
194 257,993.83 2,147.29 1,072.31 1,074.97 256,921.52 273,495.10
195 256,921.52 2,147.29 1,076.78 1,070.51 255,844.74 274,565.60

356 10,603.52 2,147.29 2,103.11 44.18 8,500.42 372,934.41
357 8,500.42 2,147.29 2,111.87 35.42 6,388.55 372,969.83
358 6,388.55 2,147.29 2,120.67 26.62 4,267.88 372,996.44
359 4,267.88 2,147.29 2,129.50 17.78 2,138.38 373,014.23
360 2,138.38 2,138.38 2,129.47 8.91 0.00 373,023.14

Figure 10.3 Fully Amortized Loan Payment Schedule

done with a personal calculator and following the algorithm:
Monthly Payment Both equations calculate the monthly
Equations Numerator payment on a loan. The main difference is
A B that equation A is stated with a negative
exponent and equation B is stated with a
r r
Pmt = PV OR Pmt = PV positive exponent. Equation A eventually
1 — (1 + r) - n 1 gets to Equation B to convert the negative

Denominator 1 − (1 + r) n ( - ) exponent to a positive value. The

Denominator with difference that you observe in B is that
arithmetic of conversion.
Negative exponent n Denominator with
Positive exponent n

Example A: Robin H. Sherwood bought a 3 acre lot for $15,000 by paying $3,000
down and securing a 15-year mortgage loan for the balance at 5.5%
interest. Calculate the uniform monthly payment that will repay the loan,
with interest, with his last payment in the fifteenth year.

Solution algorithm: Using Equation A
1. $15,000 — $3,000 = $12,000 mortgage loan

Notes on the problem are always helpful
Pmt = Monthly Payment
PV = Present Value, Loan Amount = $12,000
r = interest rate per month (Annual Interest rate ÷ payments per year, 5.5%/year =
0.055/year = ( 0.055 ÷ 12 months = ) 0.004583 (rounded to 6 places right of decimal)
n = life of loan = 15 years x 12 mo/yr =180 months; 180 payments
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