Question

You want to purchase a new car in 88 years and expect the car to cost ​$58 comma 00058,000. Your bank offers a plan with a guaranteed APR of 5.5 %5.5% if you make regular monthly deposits. How much should you deposit each month to end up with ​$58 comma 00058,000 in 88 ​years?

Answer 1

The answer is $483.33

Step-by-step explanation:

To solve this problem, we will use the following formula:

A = d((1+r/n)^nt-1)/(r/n)

Where:

r = rate (0.055)

n = number of compoundings per year (12)

nt = total number of compoundings (96)

A= d ((1+.055/12)^96-1)/(.055/12)

58,000=d(1.55)-1)/(.055/12)

58,000 = 120d

d=$483.33

Answer 2

The monthly deposit required is $2,411.

Step-by-step explanation:

We can use a financial calculator to solve the following.

The period is for 88 years thus we will make N = 88.

The interest rate is 5,5% thus we will make I/Y = 5,5$

The future value needs to be $58000. Thus FV = 58000

The present value is currently 0.

We need to calculate the monthly payments. Thus we will solve for payments (PMT).

The annual investment will be 28,939 / 12 = $2,411 per month over 88 years.

Alternatively we can use the annuity formula which is PMT = FV x i /
`(1+i)^(88)` - 1

Using this formula we also end up with an answer of 28,939. We then divide this by 12 to get the monthly amount of $2,411.