Question

(a) Investment A for $100,000 is invested at a nominal rate of interest, j, convertible semiannually. After 4 years, it accumulates to 214,358.88.

(b) Investment B for $100,000 is invested at a nominal rate of discount, k, convertible quarterly. After two years, it accumulates to 232,305.73. 2

(c) Investment C for $100,000 is invested at an annual effective rate of interest equal to j in year one and an annual effective rate of discount equal to k in year two. Calculate the value of investment C at the end of two years.

Answer 1

(a) Initial Investment = $ 100000, Compounding Frequency: Semi-Annual, Tenure = 4 years, Target Future Value = $ 214358.88

Nominal Interest Rate = j % per annum

Therefore, 100000 x [1+(j/2)]^(8) = 214358.88

[1+(j/2)]^(8) = 214358.88 / 100000 = 2.1435888

j/2 = (2.1435888)^(1/8) - 1 = 0.1

j = 0.2 or 20 %

(b)

Initial Investment = $ 100000, Compounding Frequency: Quarterly, Tenure = 2 years pr (4 x 2) = 8 quarters Target Future Value = $ 232305.73

Nominal Interest Rate = k % per annum

Therefore, 100000 x [1+(k/4)]^(8) = 232305.73

[1+(k/4)]^(8) = 232305.73 / 100000 = 2.32305.73

k/4 = (2.3230573)^(1/8) - 1 = 0.1111

k = 0.4444 or 44.44 %

(c) Initial Investment = $ 100000, Annual Effective Interest Rate for Year 1 = (1.1)^(2) - 1 = 0.21 or 21 %

Annual Effective Interest Rate for Year 2 = (1.1111)^(4) - 1 = 0.52416 or 52.416 %

Future Value of Initial Investment = 100000 x (1.21) x (1.52416) = $ 184423.11