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Mort needs to pay off a loan of $75,000 with equal payments at the end of every month over 10 years (i.e., 120 months). The annual effective rate is 5.5%. Mort decides to pay double the monthly payment each month.

How many months will it take him to pay off the loan, including the final month where the last payment will be smaller than all the rest?

Answer :

To find the number of months it will take Mort to pay off the loan, we can calculate the original monthly payment and double it to find Mort's new monthly payment. Finally, we can solve for the number of months. This calculation assumes that Mort starts making the double payments from the first month and continues until the end.

To find how many months it will take Mort to pay off the loan, we can first calculate the original monthly payment using the formula for the present value of an annuity:

PV = PMT * (1 - (1+r)^(-n))/r

Where PV is the loan amount, PMT is the monthly payment, r is the monthly interest rate, and n is the number of months. Solving for PMT, we find that PMT = PV * (r / (1 - (1+r)^(-n))).

Next, we can double the monthly payment to find Mort's new monthly payment. Finally, we can rearrange the formula to solve for n and find the number of months it will take Mort to pay off the loan.

Note: This calculation assumes that Mort starts making the double payments from the first month and continues until the end.

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Rewritten by : Barada

Final answer:

It will take Mort approximately 57 months to pay off the loan with double monthly payments.

Explanation:

To calculate the number of months it will take Mort to pay off the loan with double monthly payments, we can use the formula for the present value of an annuity:

PV = PMT * (1 - (1 + r)^(-n)) / r

Where:

  • PV is the present value (loan amount)
  • PMT is the monthly payment
  • r is the monthly interest rate
  • n is the number of months

By rearranging the formula, we can solve for n:

n = -log(1 - (PV * r) / PMT) / log(1 + r)

Using this formula, we can calculate the number of months it will take Mort to pay off the loan with double monthly payments.

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