Asked by Anh Thy Nguy?n Ng?c on Apr 29, 2024
Verified
A loan of $16,525 at 10.8% compounded monthly is to be paid off by equal monthly payments of $650. How long will it take to pay off the loan?
A) 26 months
B) 29 months
C) 32 months
D) 36 months
E) 48 months
Monthly Payments
Regular payments made every month, commonly associated with loans, mortgages, or subscription services.
Loan
A sum of money that is borrowed, typically from a financial institution, which is expected to be paid back with interest.
- Assess the payment sizes needed for loans and mortgages across diverse interest rates and repayment timeframes.
- Estimate the length of time required for payments or withdrawals concerning investments and loans, factored through compound interest calculations.
Verified Answer
DB
Diana BetancourthMay 04, 2024
Final Answer :
B
Explanation :
To determine the time it will take to pay off the loan, we can use the loan amortization formula, which is a form of the present value of an annuity formula. The formula to calculate the number of payments (n) is: n=log(PMTPMT−PV×r)log(1+r) n = \frac{\log(\frac{PMT}{PMT - PV \times r})}{\log(1 + r)} n=log(1+r)log(PMT−PV×rPMT) where:- PMT = monthly payment amount = $650- PV = present value of the loan = $16,525- r = monthly interest rate (annual rate divided by 12) = 10.8% / 12 = 0.9% = 0.009Plugging the values into the formula: n=log(650650−16525×0.009)log(1+0.009) n = \frac{\log(\frac{650}{650 - 16525 \times 0.009})}{\log(1 + 0.009)} n=log(1+0.009)log(650−16525×0.009650)n≈29 n \approx 29 n≈29 Therefore, it will take approximately 29 months to pay off the loan, making choice B the correct answer.
Learning Objectives
- Assess the payment sizes needed for loans and mortgages across diverse interest rates and repayment timeframes.
- Estimate the length of time required for payments or withdrawals concerning investments and loans, factored through compound interest calculations.