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Answer :
Final answer:
To find the number of months needed to pay off the loan, calculate the monthly interest rate, apply the formula for the number of periods, and solve for the total number of payments. The correct option is a) 71 months.
Explanation:
To determine how long it will take John to pay off the loan, we can use the formula for the number of periods to pay off a loan:
- Calculate the monthly interest rate: 8% annual interest rate compounded monthly is 8%/12 = 0.6667% monthly interest rate. Use the formula N = -log(1 - (PV times r) / PMT) / log(1 + r) where PMT is the monthly payment, PV is the loan amount, r is the monthly interest rate, and N is the total number of payments.
- Plugging in the values, N = -log(1 - (10000 imes 0.006667) / 190) / log(1.006667) ≈ 71 months.
Therefore the correct option is a) 71 months.
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