Question

A young engineer wishes to become a millionaire by the time she is 60 years old. She believes that by careful investment she can obtain a 15% annual rate of return. She plans to add a uniform sum of money to her investment program each year, beginning on her 20th birthday and continuing through her 59th birthday. How much must the engineer set aside in this project each year?

Answer 1

Answer:

$488.77

Explanation:

Present value (PV) of the amount a day to his 60th birth day = Target amount ÷ (1 + r)^n ..................... (1)

Where;

r = interest rate = 15% or 0.15

n = number of year = 1

Substituting the values into equation (1), we have:

PV of the amount a day to his 60th birth day =  $1,000,000 ÷ (1 + 0.15)^1 = $869,565.217391304.

To calculate the payment to make each year, we use the sinking fund formula as follows:

A = F * {r/[(1 + r)^n - 1]} ...................................... (2)

Where;

A = Annual payment

F = PV of the amount a day to his 60th birth day = $869,565.217391304.

r = interest rate = 15% or 0.15

n = number of years = 40

Substituting the values into equation (2), we have:

A = $869,565.217391304 * {0.15/[(1 + 0.15)^40 - 1]} = $488.77

Therefore, the engineer must set aside $488.77 in this project each year.