Answer:
a. $224.93
b. $53,983.20
c. 46.3% to principal; 53.7% to interest
Explanation:
You want the monthly payment, total repaid, and percentages to principal and interest for a 20-year $25,000 student loan at 9%.
a. Payment
The amount of the payment is given by the formula ...
A = P(r/n)/(1 -(1 +r/n)^(-nt))
where P is the principal amount at interest rate r compounded n times per year for t years.
For this loan, the monthly payment is ...
A = $25000(0.09/12)/(1 -(1 +0.09/12)^(-12·20)) ≈ $224.93
The monthly payment is $224.93.
b. Total repaid
The 240 monthly payments add up to ...
240·$224.93 = $53983.20
The total amount paid over the term of the loan is about $53,983.20.
c. Principal and Interest
The fractions of the amount repaid that go to principal and interest are ...
to principal: 25000/53983.20 ≈ 46.3%
to interest: (53983.20 -25000)/53983.20 ≈ 53.7%
About 46.3% goes to principal, and 53.7% goes to interest.
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Additional comment
The payment amount is rounded down, so there will be a slight addition to the last payment. We estimate this to be about $1. Here, we have ignored that adjustment.
For a loan of this APR and duration, it is not uncommon to pay more to interest than to principal.
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