Question

You are graduating from college and decide to buy a new car today. You plan to buy a car worth $60,000 and decide to finance your purchase. Currently, the dealership is offering a flexible financing plan in which you only need to make a payment of $7,000 at the end of every year for the next 10 years. The remaining balance will be due as a one-time payment (balloon payment) at the end of the 10th year. Given the recent COVID-19 situation, the dealership is offering some additional flexibility by allowing you to skip the first payment. However, the interest will continue to accrue during this period. You decide to take this offer and will make your payments starting exactly two years from today. At the end of the 10th year, you receive a bill for the balloon payment. You plan to finance the balloon payment with a five-year loan requiring annual payments starting exactly one year from the date you receive the balloon payment bill. Assume the interest rate for the car financing and the bank loan are both at a 7% APR compounded quarterly. What would be the payment amount for the five-year loan? Do NOT round to less than three decimal places in the intermediate steps. Round your final answer to two decimal places.

Answer 1

First of all we will calculate the effective annual rate of interest

Effective Rate = (1 + 0.07/4)^4 = 7.186%

Year	Opening Balance	Interest @7.186%	Instalment	Closing Balance
1	60,000.00	4,311.60	0	64,311.60
2	64,311.60	4,621.43	7000	61,933.03
3	61,933.03	4,450.51	7000	59,383.54
4	59,383.54	4,267.30	7000	56,650.84
5	56,650.84	4,070.93	7000	53,721.77
6	53,721.77	3,860.45	7000	50,582.22
7	50,582.22	3,634.84	7000	47,217.05
8	47,217.05	3,393.02	7000	43,610.07
9	43,610.07	3,133.82	7000	39,743.89
10	39,743.89	2,856.00	7000	35,599.89

After 10 year we will have to make a baloon payment of 35,599.89

Annual Instalment = Loan Amount / Present Value Annuity Factor 7.186%, 5 Years

Annual Instalment = 35,599.89 / 4.0798 = 8725.766

Amortization of 5 Year loan

Year	Opening Balance	Interest @7.186%	Instalment	Closing Balance
1	35,599.89	2,558.21	8725.7663	29,432.33
2	29,432.33	2,115.01	8725.7663	22,821.57
3	22,821.57	1,639.96	8725.7663	15,735.76
4	15,735.76	1,130.77	8725.7663	8,140.77
5	8,140.77	585.00	8725.7663	0.00