javier borrows $50,000 from a local bank at an APR of 9%, compounded monthly. His monthly payments amount to $50,000 (A/P, 0.75%, 60)=$1,040 for a 60-month loan. If Javier makes an extra payment on the first month of each year, his repayment duration for the loan will be reduced by how many months?

Question

Javier borrows $50,000 from a local bank at an APR of 9%, compounded monthly. His monthly payments amount to $50,000 (A/P, 0.75%, 60)=$1,040 for a 60-month loan. If Javier makes an extra payment on the first month of each year, his repayment duration for the loan will be reduced by how many months?

Accepted Answer

We can solve for N using trial and error. If we guess N = 53 months, we’ll find that economic equivalence is established with the following relationship:
$50,000 = $1,040(P/A, [latex]^{3}/_{4}[/latex]%, 53) + $1,040(P/F, [latex]^{3}/_{4}[/latex]%, 1)

+ $1,040(P/F, [latex]^{3}/_{4}[/latex]%, 13)

+ $1,040(P/F,[latex]^{3}/_{4}[/latex]%, 25) + $1,040(P/F, [latex]^{3}/_{4}[/latex]%, 37)

+ $1,040(P/F, [latex]^{3}/_{4}[/latex]%, 49)
So N = 53 months. This means that five extra payments will reduce the loan period from 60 months to 53 months. This is a net savings of two payments ($2,080) over the loan’s duration. If Javier can earn more than [latex]^{3}/_{4}[/latex]% per month on his money, he should not make extra payments on this loan.

Question 5.II: javier borrows $50,000 from a local bank at an APR of 9%, co...

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