Question

You hope to buy your dream car seven years from now, which is expected to cost $110,000 at that time. You will set aside a fixed amount every year to a sinking fund that earns 9% interest to collect this amount, starting from the end of the first year. How much should you deposit at the end of each year to be able to buy the car?

A) $11,955.96
B) $9,974.18
C) $9,618.84
D) Answers A, B and C are not correct

Answer 1

To buy your dream car in 7 years, you should deposit approximately $12,223.30 at the end of each year.

Step-by-step explanation:

To calculate the amount you need to deposit at the end of each year, you can use the formula for the future value of an annuity:

FV = P*((1+r)^n-1)/r

Where FV is the future value, P is the annual deposit, r is the interest rate per period, and n is the number of periods. In this case, you want to have $110,000 in 7 years with an interest rate of 9% per year. Plugging these values into the formula:

FV = P*((1+0.09)^7-1)/0.09 = $110,000

Rearranging the equation:

P = $110,000 * (0.09/((1+0.09)^7-1))

Calculating this expression gives:

P ≈ $12,223.30

Therefore, you should deposit approximately $12,223.30 at the end of each year to be able to buy your dream car in 7 years.