Question

Derek plans to retire on his 65th birthday. However, he plans to work part-time until he...

Derek plans to retire on his 65th birthday. However, he plans to work part-time until he turns 72.00. During these years of part-time work, he will neither make deposits to nor take withdrawals from his retirement account. Exactly one year after the day he turns 72.0 when he fully retires, he will wants to have \$3,397,041.00 in his retirement account. He he will make contributions to his retirement account from his 26th birthday to his 65th birthday. To reach his goal, what must the contributions be? Assume a 9.00% interest rate.

The amount of annual contribution is \$5046

Explanation:

Interest rate = 9%

Amount required in 73th year = \$3,397,041

Step 1: - calculation of Future Value Annuity (value of required amount I in 65th year)

value of required amount I in 65th year = Amount required in 73th year / (1+ i)n

here,

Amount required in 73th year = \$3,397,041

I = 9%

N = 8 (73 – 65)

By substituting the values, we get

FV A = \$3,397,041(1+.09)8

FV A=1,704,860

Step 2 : - calculation of equal contributions

FV A = A * {(1 + r)^n - 1} / r

Here,

FV A = \$1,704,860

r = 9%

n = 40 (26th year to 65th year)

A = ?

By substituting the values in the equation, we get,

\$1,704,860= A * {(1+.09)40 - 1} / .09

\$1,704,860= A * (1.0940 - 1} / .09

\$1,704,860= A * 31.40942005/ .09

\$1,704,860= A * 337.88

A =\$1,704,860 / 337.88

A = \$5046