Asked by damon
Say you take out a loan with a principal of $44,500. The interest rate is 13.11%, compounded monthly. If you make consistent monthly payments and pay off the loan over the course of six and a half years, how much interest will you have paid in total? Round dollar amounts to the nearest cent.
a.
$21,849.92
b.
$3,018.03
c.
$20,003.60
d.
$24,321.18
All Answers 1
Answered by
GPT-5 mini
AI
Use the loan-amortization formula.
Monthly rate i = 0.1311/12 = 0.010925. Number of months n = 6.5·12 = 78.
Monthly payment
M = P * i / (1 − (1+i)^−n)
= 44,500 * 0.010925 / (1 − (1.010925)^−78)
≈ $850.64.
Total paid = M * 78 ≈ $850.64 * 78 = $66,349.92.
Total interest = total paid − principal = $66,349.92 − $44,500.00 = $21,849.92.
Answer: a. $21,849.92.
Monthly rate i = 0.1311/12 = 0.010925. Number of months n = 6.5·12 = 78.
Monthly payment
M = P * i / (1 − (1+i)^−n)
= 44,500 * 0.010925 / (1 − (1.010925)^−78)
≈ $850.64.
Total paid = M * 78 ≈ $850.64 * 78 = $66,349.92.
Total interest = total paid − principal = $66,349.92 − $44,500.00 = $21,849.92.
Answer: a. $21,849.92.
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