Question

Helen invested the profit of her business in an investment fund that was earning 3.25% compounded monthly. In 3 years, she began withdrawing $3,500 from this fund at the end of every 6 months. If the money in the fund lasted for the next 4 years, how much money did she initially invest in the fund?

(P.s the answers posted before are wrong)

Answer 1

Helen began withdrawing from Fund every 6 months = $3500

Interest Rate on Inverstment fund = 3.25% compounded monthly

calculating 6 monthly rate from compounded monthly:-

where, R = Interest Rate = 3.25%

m = No of times compunded in a year = 12

n = no of period = 6

r = 6-monthly rate

r = 1.6360%

Calculating the Present Value of withdrawals at t=3:-

Where, C= Periodic withdrawals = 3500

r = Periodic Interest rate = 1.6360%

n= no of periods = 4 years*2 = 8

Present Value = $26,472.30

Now, Calculating the Present Value at t= 0 from t= 3:-

where, PV3 = $26,472.30

r = interest rate = 0.016360

n = no of periods = 3 years*2 = 6

PV0 = $24016.31

So, Money she initial invested = $24,016.31