Question

When you purchased your? car, you took out a? five-year annual-payment loan with an interest rate of 5.7% per year. The annual payment on the car is $4,900.

You have just made a payment and have now decided to pay off the loan by repaying the outstanding balance. What is the payoff amount for the following? scenarios?

a.You have owned the car for one year? (so there are four years left on the? loan)?

b. You have owned the car for four years? (so there is one year left on the? loan)?

2. Your grandmother has been putting $5,000 into a savings account on every birthday since your first? (that is, when you turned? one). The account pays an interest rate of 9%.

How much money will be in the account immediately after your grandmother makes the deposit on your 18th birthday

Answer 1

1) Using excel sheet below
a) Pay off after one year = 17096.31
b)Pay off after four years = 4635.76

	Formulas	PMT FUNCTION= PMT(0.55%,360,570,000)	InterestPaid = Interest rate per period * beginning balance	Beginning balance - Interest Period	Ending Balance = Beginning Balance - Principal Paid
Payment No	Beginning balance	Payment Amount	Interest Paid	Principal Paid	Ending Balance
1	20,810.13	$4,900.00	1186.18	$3,713.82	$17,096.31
2	17,096.31	$4,900.00	974.49	$3,925.51	$13,170.80
3	13,170.80	$4,900.00	750.74	$4,149.26	$9,021.53
4	9,021.53	$4,900.00	514.23	$4,385.77	$4,635.76
5	4,635.76	$4,900.00	264.24	$4,635.76	($0.00)

2)Amount of money deposited by grandmother till 18th birthday = money deposited on birthday + FV of 17 annuities of $5000 = 5000 + 5000 *[(1+r)ⁿ-1]/r = 5000 + 5000*[(1+9%)-1]/9% =5000+ 184868.82 = 189868.20