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?

Group of answer choices

(1) $26 751, (2) $35 119, (3) 5.79%

(1) $25 899, (2) $36 160, (3) 5.80%

(1) $27 029, (2) $35 119, (3) 2.66%

(1) $26 751, (2) $35 486, (3) 5.79%

(1) $25 899, (2) $36 160, (3) 6.10%

(1) $27 029, (2) $35 486, (3) 5.91%

Answer 1

(1) $26 751, (2) $35 119, (3) 5.79%

(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%