g Robert Hitchcock is 40 years old today and he wishes to accumulate $500,000 by his 65th birthday so he can retire to his summer place on Lake Hopatcong. He wishes to accumulate this amount by making equal deposits on his 40th through his 64th birthdays. What annual deposit must Robert make if the fund will earn 8% interest compounded annually

The correct answer is $6934.48.

Explanation:

According to the scenario, the given data are as follows:

Time period (41 - 64 years) (n) = 24 years

Rate of interest (r) = 8%

Future value (FV) = $500,000

Annual deposit amount = P

So, we can calculate the annual deposit amount by using following formula:

FV = P * (1+r) * [{ (1+r) ^n - 1} : r]

By putting the value, we get

$500,000 = P * (1 + 0.08) [{ (1+0.08) ^24 - 1} : 0.08]

$500,000 = P * (1.08) [{ (1.08) ^24 - 1} : 0.08]

$500,000 = P * (1.08) [{ 6.34118073724 - 1} : 0.08]

$500,000 = P (72.1035)

P = $500,000 : 72.1035

P = 6934.48