Complete an amortization schedule for a $30,000 loan to be repaid in equal installments at the end of each of the next three years. The interest rate is 9% compounded annually. If an amount is zero, enter "0". Do not round intermediate calculations. Round your answers to the nearest cent.
Beginning | Repayment | Ending | |||
Year | Balance | Payment | Interest | of Principal | Balance |
1 | $ | $ | $ | $ | $ |
2 | |||||
3 |
What percentage of the payment represents interest and what percentage represents principal for each of the three years? Do not round intermediate calculations. Round your answers to two decimal places.
% Interest | % Principal | |
Year 1: | % | % |
Year 2: | % | % |
Year 3: | % | % |
Why do these percentages change over time?
a) Amortization
Schedule
Equal Annual Installment = Loan Amount / PVAF = $30,000 / 2.531295
= $11,851.64
PVAF is the sum of present value of annuity for 3 years
Year | Beginning balance | Installment | Interest (Op bal * 9%) |
Principal (installment - int) |
Ending
Balance (Op bal - Principal) |
1 | $30,000 | $11,851.64 | $2,700 | $9,151.64 | $20,848.36 |
2 | $20,848.36 | $11,851.64 | $1876.35 | $9,975.29 | $10,873.07 |
3 | $10,873.07 | $11,851.65 | $978.57 | $10,873.07 | 0 |
b) Computation of
% of payment which represents principal and
interest
Year1 | % Interest | % Principal |
1 | 22.78% | 77.22% |
2 | 15.83% | 84.17% |
3 | 8.26% | 91.74% |
c) These percentages changes overtime because even though
the total payments is constant the amount of interest paid each
year is declining as the remaining or oustanding balance
declines.
Option I is correct
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