Question

James Perkins wants to have a million dollars at retirement, which is 15 years away. He already has $200,000 in an IRA earning 8 percent annually. How much does he need to save each year, beginning at the end of this year, to reach his target

Answer 1

Solution :

Given :

James needs $ 1,000,000 after 15 years.

His IRA deposit is $ 200,000 and is earning at the rate of 8% per annum.

Maturity value of $200,000 after 15 years = $2000000 \times( 1.08)^{15}$

                                                                     = $ 634,434.

Balance fund needed after 15 years = 1,000,000 - 634,434

                                                           = $ 365,566

Therefore, the future value of the annuity is :

$FV=A[\frac{(1+k)^n-1}{k}]$

Here, FV = future annuity value = 365,566

            A = periodical investment

            k = interest rate = 8%

            n = period = 15 years

∴$365566 = A\frac{[(1.08)^{15}-1]}{0.08}$

       A = 13,464

Thus, James needs to save $ 13,464 each year end to reach his target.