Angela borrowed $30,000 for her college tuition at 3% per year convertible quarterly. Her father agreed to make payments until the outstanding balance was less than $10,000. At that time Angela would make payments until the loan would be repaid. The length of the loan is for 15 years and level payments are made on an annual basis. How many payments will Angela need to make

4 payments

Explanation:

Loan amount = 30,000

Nominal annual interest rate = 3% = 0.03

Effective annual interest rate = (1+0.03/4)^4 - 1 = 1.0075^4 - 1 = 1.03033919066 - 1 = 0.03033919066 = 3.03%

No of annual payment = 15

Annual payment = PMT(Effective annual interest rate, No of annual payment, -Loan amount, 0)

Annual payment = PMT(3.03%, 15, -30,000, 0)

Annual payment = $2,519.17

Remaining balance = $10,000

Number of annual payments to get desired remaining balance = Nper(Effective annual interest rate, -Annual payment, Loan amount, -Remaining balance, 0)

= Nper(3.03%, -2,519.17, 30,000, -10,000, 0)

= 11

Number of annual payments to get desired remaining balance = 11. So, number of annual payment Angela need to make is 4 (15-11).

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