Ivana Beerich just turned 20 and received a gift of $50,000 from her rich aunt.

Question

Ivana Beerich just turned 20 and received a gift of $50,000 from her rich aunt. Ivana likes to plans ahead and would like to retire on her 55 birthday. She thinks she’ll need to have about $2,000,000 saved by that time in order to maintain her lavish lifestyle. She plans to make a deposit at the end of each month until she is 50 into an account that she’ll open with her aunt’s gift. After age 50, she plans to stop making deposits and let the money grow until it reaches $2,000,000 when she turns 55. Assume she can earn 7% compounded semi-annually. How much will Ivana have to deposit into her account each month to achieve her objective?

Explanation / Answer

FV of 50,000 growing for 35 years + FV of monthly deposit from from age 20 to age 50 = 2000000

50000*(1.035)^70 + x*(1.035)^10 = 2,000,000

X = 1023933.08

Now X is the future value of monthly deposits from age 20 to age 50

(1.035)^2 -1 = 7.12%

Now calculating monthly interest

(1.0712)^1 =(1+x)^12

x = 0.58%

Now calculating monrhlt deposits

=PMT(0.0058,360,0,1023933.08,0) =845.956

0.58% is the monthly interest

1023933.08 is the future value

360 is the time period

Therefore he has to deposit 845.96 each month

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