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The loan amortization formula can be used, which is also known as
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The loan amortization formula can be used, which is also known as the formula for calculating the equal payment amount for an amortizing loan, to determine Lisa’s loan’s annual payments over the course of five, ten, or twenty years of amortization (Caplinger, 2023).
For a loan that amortizes, the annual payment (A) can be calculated using the following formula:
A= P x r x (1+r)n
(1+r)n -1
5 year term:
Monthly interest rate = 7% / 12 = 0.583%
Number of payments = 5 x 12 = 60
Monthly payment = $10,000 x (0.00583 x (1 + 0.00583) ^ 60) / ((1 + 0.00583) ^ 60 – 1) = $198.01
Annual payment = $198.01 x 12 = $2,376.14
10 year term:
Monthly interest rate = 7% / 12 = 0.583%
Number of payments = 10 x 12 = 120
Monthly payment = $10,000 x (0.00583 x (1 + 0.00583) ^ 120) / ((1 + 0.00583) ^ 120 – 1) = $116.11
Annual payment = $116.11 x 12 = $1,393.30
20 year term: Monthly interest rate = 7% / 12 = 0.583%
Number of payments = 20 x 12 = 240
Monthly payment = $10,000 x (0.00583 x (1 + 0.00583) ^ 240) / ((1 + 0.00583) ^ 240 – 1) = $77.53
Annual payment = $77.53 x 12 = $930.36
Therefore, as the loan term increases, the monthly payment decreases, but the total interest paid over the life of the loan increases. This is because you’re spreading the loan out over more payments.
Year
Beginning Balance
Payment
Interest
Principal
Ending Balance
1
$10,000,000.00
$1813,327.23
$700,000.00
$1,113,327.23
$8,886,672.77
2
$8,886,672.77
$1813,327.23
$622,067.09
$1,191,260.14
$7,695,412.63
3
$7,695,412.63
$1813,327.23
$538,678.88
$1,274,648.35
$6,420,764.28
4
$6,420,764.28
$1813,327.23
$449,451.50
$1,363,875.73
$5,056,888.55
5
$5,056,888.55
$1813,327.23
$354,982.20
$1,458,345.03
$3,598,543.52
If Lisa accepts Richard’s offer for a ten-year, 7% interest-only loan, her annual payment will consist only of the interest on the loan amount, and she won’t be paying off any principal.
Annual Interest Payment=Principal x Interest Rate x Annual Interest Payment=Principal x Interest
Rate
Given:
Principal amount (P) = Amount Lisa borrows
Interest rate (r) = 7% per year
Since it’s an interest-only loan, Lisa’s annual payment will be:
Annual Payment=P x r
Lisa’s annual payment will be:
Annual Payment=$10,000,000×0.07=$700,000Annual Payment=$10,000,000×0.07=$700,000
So, Lisa’s annual payment will be $700,000 for each of the ten years.
Pattern of Payments over the Ten Years:
Lisa’s payments will remain consistent at $700,000 each year.
Since it’s an interest-only loan, the principal amount remains unchanged over the ten-year period.
Regarding Richard’s reinvestment of the interest payments:
If Richard can reinvest the interest payments at a rate of 7% per year, he will have accumulated the total amount of interest earned over the ten years.
Since the interest rate is 7%, the interest earned each year will be $700,000.
Over ten years, Richard’s total accumulated amount from reinvesting the interest payments would be the sum of the interest payments compounded annually:
Total Amount=Annual Interest Payment×((1+Interest Rate)−1)Total Amount=Annual Interest Payment x ((1+Interest Rate) n−1)
Where:
Annual Interest Payment = $700,000
Interest Rate= 7%
n = 10 years
Total Amount=$700,000 x ((1+0.07)10−1) Total Amount=$700,000 x ((1+0.07)10−1)
Total Amount=$700,000 x (1.0710−1) Total Amount=$700,000 x (1.0710−1)
Total Amount=$700,000 x (1.967151−1) Total Amount=$700,000 x (1.967151−1)
Total Amount≈$1,376,005.70
So, Richard would have approximately $1,376,005.70 at the end of the tenth year if he reinvests the interest payments at a rate of 7% per year.
Caplinger, D. (2023, July 17). How is a loan amortization schedule calculated? The Motley Fool. https://www.fool.com/the-ascent/personal-finance/how-is-loan-amortization-schedule-calculated/