Question

Mikolas Proude is seeking to establish an investment portfolio with 2 investments. These are a zero coupon bond with the government authority, Sandgrid, requiring an initial investment of $5 000 and a high interest deposit with the Stateside Bank requiring an initial investment of $15 000. The zero coupon bond accumulates interest at 9% p.a. compounded monthly for a 10-year term and has an upfront fee of $50 subtracted from the initial investment. The high interest deposit with the Stateside Bank earns interest at 5% p.a. compounded half-yearly for a 5-year term and has a fee payable on maturity of $200 subtracted from the investment value. It is expected that Mikolas will be able to reinvest the initial investment in Stateside Bank at the end of 5 years into a further high interest deposit for another 5-year term at 4% p.a. compounded quarterly. This further deposit also has a fee payable on maturity of $200 subtracted from the investment value.

Required:

(1) Calculate the approximate net value of Mikolas’ portfolio at the end of 5 years.

(2) Calculate the approximate net value of Mikolas’ portfolio at the end of 10 years.

(3) What is the approximate compound annual rate of return on the portfolio?

Answer 1

(1) Calculate the approximate net value of Mikolas’ portfolio at the end of 5 years.

Value = (ZCB Investment - Deduction) * (1 + monthly Interest)^(Years * 12) + (High Interest Deposit )*(1 + Semi Annual Interest)^(Years *2) - deduction

Value = (5000 - 50) * (1 + 9%/12)^(5 * 12) + (15000)*(1 + 2.50%)^(5 *2) - deduction

Value = 4950 * 1.565681 + 15000*1.2801 - 200

Value = 7750.12 + 19201.27 -200

Value = $26751.39

(2) Calculate the approximate net value of Mikolas’ portfolio at the end of 10 years.

Value = (ZCB Investment - Deduction) * (1 + monthly Interest)^(Years * 12) + (State side Bank Deposit )*(1 + Quarterly Interest)^(Years *4) - deduction

Value = (5000 - 50) * (1 + 9%/12)^(10 * 12) + (19001.27)*(1 + 1%)^(5 *4) - 200

Value = 4950 * 2.451357 + 19001.27*1.2202 - 200

Value = $35119.38

(3) What is the approximate compound annual rate of return on the portfolio? = 5.79%