Question

The Flemings secured a bank loan of $312,000 to help finance the purchase of a house. The bank charges interest at a rate of 5%/year on the unpaid balance, and interest computations are made at the end of each month. The Flemings have agreed to repay the loan in equal monthly installments over 25 years. What should be the size of each repayment if the loan is to be amortized at the end of the term

Answer 1

The size of each repayment should be $1,823.92

Step-by-step explanation:

The periodic payment of loan is a form of annuity cash flow.

Use the following formula to calculate the size of the payment

PV of Annuity = Annuity Payment x ( 1 - ( 1 + interest rate )^-Numbers of periods ) / Interest rates

Where

Interest rate = Monthly interest rate = 5% / 12

Numbers of periods = Numbers of monthly payments = 25 years x 12 months per years = 300

PV of Annuity = Bank loan value = $312,000

Annuity Payment = Size of repayment = ?

Placing values in the formula

$312,000 = Size of repayment x ( 1 - ( 1 + 5%/12 )^-300 ) / 5%/12

$312,000 = Size of repayment x 171.060047

Size of repayment = $312,000 / 171.060047

Size of repayment = $1,823.92093

Size of repayment = $1,823.92