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}](https://tex.z-dn.net/?f=2000000%20%5Ctimes%28%201.08%29%5E%7B15%7D)
= $ 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}]](https://tex.z-dn.net/?f=FV%3DA%5B%5Cfrac%7B%281%2Bk%29%5En-1%7D%7Bk%7D%5D)
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}](https://tex.z-dn.net/?f=365566%20%3D%20A%5Cfrac%7B%5B%281.08%29%5E%7B15%7D-1%5D%7D%7B0.08%7D)
A = 13,464
Thus, James needs to save $ 13,464 each year end to reach his target.