Question

George buys a car every 6 years for $18,000. He trades in his current car to count as the 20% down payment. The rest is financed at a nominal 12% in- terest with monthly payments over 6 years. When the loan is paid off, he trades in the car as the “20%” down payment on the next car, which he finances the same way.

Jeanette has similar tastes in cars, and the dealer will count her trade-in vehicle as worth 20%. She has paid cash for old cars in the past, so she now has

$14,400 in cash for the other 80% cost of a new car. In 6 years, her vehicle will be worth the “20%” down payment. She wants to make a monthly deposit so that she has the other 80% of the vehicle’s cost in 6 years. Her savings account has a nominal annual interest rate of 6% with monthly compounding.

What is George’s payment? What is Jeanette’s deposit? If Jeanette also deposits the difference in a retirement account that pays 9% nominal interest with monthly compounding, what does she have for retirement after 40 years?

Answer #1

**1)** As we are given in the question:

George buys car after every 6 years worth = $18000

Current car down payment worth= $3600

He has to pay remaining amount= $14400

It is financed at 12% interest rate.

So, George's payment= 14400*112/100

= $16128

Monthly payment= 16128/12*6

= $224

**2)** Jeanette's deposit:

Jeanette has= $14400

Car's cost= 14400*100/80

= $18000

In 6 years, 20% car down payment worth= $3600

She has to pay $14400 and has to save for the same amount till next 6 years.

So, her monthly deposit will be= 14400/6*12

= $200

Amount she gets after 6 years through saving account by compound interest:

A= P(1+r/n)^{(nt)}

= $17,654.59

Remaining amount= 17654.59 - 14400

= 3254.59

Amount she will have after retirement after 40 years (calculated through compound interest)= $1,17,522.93

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