Question

A debt of $10000 is to be repaid with quarterly installments of $4000, $3000, $2000, $1000, plus a final payment which pays off the loan after 5 quarters. Interest rate is 12% compounded quarterly. Find the outstanding balance after the second payment

Answer 1

The outstanding balance after the second quarterly installment on the $10,000 debt with a 12% annual interest rate compounded quarterly is $3,489.

Step-by-step explanation:

To calculate the outstanding balance after the second payment on a debt with quarterly installments and compounded interest, we use the remaining balance formula. Each payment reduces the balance, and interest is then added to the remaining balance.

Firstly, calculate the interest that has accrued after the first quarter:
$10,000 × (1 + 0.12/4) = $10,000 × 1.03 = $10,300.

After the first installment of $4,000, the new balance is:
$10,300 - $4,000 = $6,300.

Interest accrued after the second quarter:
$6,300 × (1 + 0.12/4) = $6,300 × 1.03 = $6,489.

After the second installment of $3,000, the new outstanding balance is:
$6,489 - $3,000 = $3,489.

The outstanding balance after the second payment is $3,489.