Question

A student borrows $95,000 for business school at 4.5% stated annual interest with monthly repayment over 9 years. Consider this as a loan with no payments or interest during school so that the problem structure is equivalent to a standard loan received one period before the first payment. Suppose that to better match expected student salary growth over time, the loan is structured as a growing annuity with each monthly payment growing by 0.3% compared to the previous monthly payment. How much is the first monthly payment

Answer 1

$918.70 or $900

Step-by-step explanation:

The computation of the first monthly payment is given below:

Interest rate per Month is

= Annual Rate ÷ 12

= 4.50% ÷ 12

= 0.375%

Now

Present Value of Growing Annuity = First payment × (1 - ((1 + Growth Rate) ÷ (1 + Interest Rate))^Periods) × 1 ÷ (Interest Rate - Growth Rate)

95000 = First payment × (1 - ((1 + 0.30%) ÷ (1 + 0.375%))^108) × 1 ÷ (0.375% - 0.30%)

95000 = First payment × (1 - 0.999252^108) × 1 ÷ (0.075%)

95000 = First payment × (1 - 0.92244) × 1 ÷ (0.075%)

95000 = First payment × 103.4067

First payment = $918.70 or $900