Question

John borrows ​$46,000 from a local bank at an APR of 9.6​%, compounded monthly. His monthly payments are ​$46,000​ (A/P,0.8​%,58​)=​$994 for a 58​-month loan. If John makes an extra payment on the first month of each​ year, his repayment duration for the loan will be reduced to how many​ months?

​John's repayment duration for the loan will be reduced to ______months

Answer 1

When an additional monthly payment is made every year there are a total of 5 additional payments This implies

46000 = 994(A/P, 0.8%, N) + 994(P/F, 0.8%, 1) + 994(P/F, 0.8%, 13) + 994(P/F, 0.8%, 25) + 994(P/F, 0.8%, 37) + 994(P/F, 0.8%, 49)

46000 - 994*(0.99206+0.9016+0.81938+0.74466+0.67676) = 994(A/P, 0.8%, N)

41890.35 = 994(A/P, 0.8%, N)

(A/P, 0.8%, N) = 42.143206

This gives N = 52 as the closest option

Hence John's repayment duration for the loan will be reduced to 52 months.