Question

1. If you deposit $15,000 per year for 23 years (each deposit is made at the end of each year) in an account that pays an annual interest rate of 12%, what will your account be worth at the end of 23 years?

2. You plan to buy a car that has a total "drive-out" cost of $21,100. You will make a down payment of $2,321. The remainder of the car's cost will be financed over a period of 4 years. You will repay the loan by making equal monthly payments. Your quoted annual interest rate is 12% with monthly compounding of interest. (The first payment will be due one month after the purchase date.) What will your monthly payment be?

Answer 1

1]

Future value of annuity = P * [(1 + r)n - 1] / r,

where P = periodic payment. This is $15,000

r = periodic rate of interest. This is 12%

n = number of periods. This is 23

Future value of annuity = $15,000 * [(1 + 12%)23 - 1] / 12%

Future value of annuity = $1,569,043.41

Value of account at the end of 23 years = $1,569,043.41

2]

Loan amount = cost of car - down payment = $21,100 - $2,321 = $18,779

Total number of monthly payments = number of years * 12 = 4 * 12 = 48

PV of annuity = P * [1 - (1 + r)-n] / r,

Here, PV = loan amount = $18,779

P = periodic payment, which needs to be calculated

r = periodic interest rate = 12%/12 = 1%

n = total number of periods = 48

$18,779 = P * [1 - (1 + 1%)-48] / 1%

P = ($18,779 * 1%) / [1 - (1 + 1%)-48]

P = $494.52

monthly payment = $494.52