Question

You want to save $98,000 to buy an boat by making an equal, end of year payment into a brokerage account for the next 9 years. If you expect to earn an annual interest rate of 7.75% on your account, how much do you need to deposit each year into your account?

Answer 1

Answer: $7,930

Explanation:

The payments are to be equal so this is an annuity. The expected value is to be $98,000 in 9 years so this is a future value of an Annuity.

The formula is;

FV = $P * \frac{[1 + i]^n-1}{i}$

98,000 = $P * \frac{[1 + 0.075]^9-1}{0.075}$

98,000 = P * 12.3581

P = 98,000/12.3581

P = $7,930

Answer 2

Answer:

Annual deposit= $7,930.11

Explanation:

Giving the following information:

FV= $98,000

n= 9 years

i= 0.0775

To calculate the annual deposit, we need to use the following formula:

FV= {A*[(1+i)^n-1]}/i

A= annual deposit

Isolating A:

A= (FV*i)/{[(1+i)^n]-1}

A= (98,000*0.0775) / [(1.0775^9) - 1]

A= $7,930.11