Suppose that you have a $15,000 balance on a car loan. The balance accrues interest annually at a rate of 7% of the total unpaid balance at the end of the year. So the balance in one year depends on the current balance, the interest rate, and the payment: New balance = (Previous balance payment) · (1 + i) For example, if you make a $2,500 payment in the first year, then your balance next year will be ($15,000 $2,500) · 1.07 = $13,375. Note that if you make the same payment each year, then after T years, the balance will be:1 Year T balance = (Initial balance) · (1 + i) T payment · (1 + i) T +1 (1 + i) Answer the following: (a) iii. What is the cumulative dollar value of the interest that you will end up paying to your lender? (B) Suppose that you wish to pay off your loan in 5 years. i. What is the minimum annual payment required? ii. What is the cumulative dollar value of the interest that you will end up paying to your lender?
Solution
the cumulative dollar value of the interest that you will end up paying to your lender as follows
B) minimum annual payment required
minimum annual payment required is $ 3,658
.
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Suppose that you have a $15-000 balance on a car loan- The balance acc.docx
1. Suppose that you have a $15,000 balance on a car loan. The balance accrues interest annually at
a rate of 7% of the total unpaid balance at the end of the year. So the balance in one year depends
on the current balance, the interest rate, and the payment: New balance = (Previous balance
payment) · (1 + i) For example, if you make a $2,500 payment in the first year, then your
balance next year will be ($15,000 $2,500) · 1.07 = $13,375. Note that if you make the same
payment each year, then after T years, the balance will be:1 Year T balance = (Initial balance) ·
(1 + i) T payment · (1 + i) T +1 (1 + i) Answer the following: (a) iii. What is the cumulative
dollar value of the interest that you will end up paying to your lender? (B) Suppose that you wish
to pay off your loan in 5 years. i. What is the minimum annual payment required? ii. What is the
cumulative dollar value of the interest that you will end up paying to your lender?
Solution
the cumulative dollar value of the interest that you will end up paying to your lender as follows
B) minimum annual payment required
minimum annual payment required is $ 3,658
Year Loan amount Interest@7% Repayment Balance
1 15000 1050 2500 13550
2 13550 949 2500 11999
3 11999 840 2500 10338
4 10338 724 2500 8562
5 8562 599 2500 6661
6 6661 466 2500 4628
7 4628 324 2500 2452
8 2452 172 2500 123
Total Interest to be paid 5123
