Question

A bank offers you a $1M loan with an IRR of 4% (i.e. the bank makes a return of 4% on the loan). The bank requires you to repay the loan in 14 equal annual installments, starting next year.(a) What is the annual payment on the loan, to the nearest dollar

Answer 1

Answer:

$94,669 approx

Explanation:

Given: Amount of Loan =  $1 million

          Internal Rate of Return = 4%

           Period = 14 years

Assumption: It has been assumed this being a case of deferred annuity wherein annual installments are payable at the end.

Equated Annual Investment =  Borrowed Sum/ Cumulative present value of cash flows for 14 years

Cumulative present value factor at the rate of 4% for 14 years is calculated using the following formula.

= $\frac{1}{(1\ +\ .04)^{1} } \ +\ \frac{1}{(1\ +\ .04)^{2} } \ +\ ......+\ \frac{1}{(1\ +\ .04)^{14} }$ = 10.5631

Equated Annual Installment = $10,00,000/10.5631  

Equated Annual Installment each year = $10,00,000/10.5631 = $94,669 approx.