Alistair deposited $10,000 on July 1, 2005, in a first fund that gives interest

Question

Alistair deposited $10,000 on July 1, 2005, in a first fund that gives interest of 31?2 percent compounded semiannually and matures on June 1, 2012. He knows that, on December 18, 2012, he can deposit money in a second fund that will pay interest of 3.96 percent compounded quarterly and will mature on February 18, 2038. Between the maturity date of the first fund and the start date of the second fund, he can earn interest of two percent in a short-term deposit fund. If Alistair wants to receive $50,000 on the maturity date of the second fund, determine the amount he must deposit on June 1, 2012, in the short- term deposit fund in addition to the amount he will receive from the first fund.

Explanation / Answer

Alistairs capital after first fund = 10000*(1+0.035/2)^(13.8333) = $ 12,712.35

(13.8333 is the number of semiannual periods from July 1, 2005 to June 1, 2012.)

Let him invest X more.

Total amoun for 2nd fund after investment = (12712.35+X)*(1.02)

Hence his final value at 18 feb 2038 = (12712.35+X)*(1.02)*(1+0.0396/4)^(100+2/3) = 50000

(100+2/3 is the number of quarter periods from December 18, 2012 to February 18, 2038)
Hence, Invested amount = $ 5,471.271

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