You are loaned $100,000 and pay this back by making constant payments at the end of each year for 40 years.

You are loaned $100,000 and pay this back by making constant payments at the end of each year for 40 years. If effective annual interest is i = 3% then find when the outstanding balance first falls below $50,000.

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Expert Solution

A loan repays itself by a fixed payment every year. We have to find when the outstanding balance falls below 50,000 for the first time.

When a loan is amortized under a fixed payment, a part of the payment goes towards reducing the balance of the loan. Hence, the balance outstanding keeps falling throughout the term of the loan.

First we will calculate the annual payment, P on the loan.

Let us assume that outstanding balance falls below B = 50,000 for the firs time when there are still m payments left to be done.

Then the balance loan = PV of the m remaining payment P as annuity

Hence, the loan balance will fall below 50,000 for the first time after 26 years.

Junaid answered 1 year ago

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