Question

A loan at 6.5% annually has an initial payment of 300, and 9 further payments. The payment amount increases by 20 each year. Find the loan balance immediately after the 6th payment.

Answer 1

Initial payment = $300
Payment amount increase by $20 each year
First six payments = $300 , $320, $340, $360, $380, $400
Remaining payments = $420, $440, $460, $480
The outstanding loan balance is the sum of all the present values of remaining payments

Loan balance = $420/(1+0.065) + $440/(1+0.065)^2 + $460/(1+0.065)^3 + $480/(1+0.065)^4
= $394.37 + $387.94 + $380.83 + $373.11
= $1,536.22 or $1,536
Loan balance immediately after the 6th payment = $1,536.22 or $1,536 (approx).