Question

Problems Al. Assume that you have $4,000 invested in an account today (that is, year 0). Calculate the future value of this amount at the end of each of the following time horizons and interest rates: a) End of three years at an interest rate of 6% per annum. b) End of six years at an interest rate of 6% per annum. c) End of three years at an interest rate of 12% per annum Tutorial Questions for Week 1's Lecture FNCE10002 Principles of Finance Semester 1, 2020 d) Note that the time horizon in part (a) is half the time horizon in part (b) but the total amount of interest earned in part (a) is less than half the amount of interest earned in part (b). Why is this the case? Explain. e) Provide a breakup of the total interest, simple interest and interest-on-interest eamed in parts (a) and (b).

Answer 1

a) End of three years, Future Value (Assuming Annual Compounding) = Present Value *( 1+ Interest Rate)^3 = $4,764.06.

b) End of six years, Future Value (Assuming Annual Compounding) = Present Value *( 1+ Interest Rate)^6 = $5,674.08.

c) End of three years, Future Value (Assuming Annual Compounding) = Present Value *( 1+ Interest Rate)^3 = $5,619.71.

d) Interest earned in part (a) = Future Value - Present Value = $ 764.06. Interest earned in part (b) = Future Value - Present Value = $1,674.08. If there was no compounding, then interest in part (a) would have been half of interest in part (b) but because of compounding, interest-on-interest is earned. As time progresses, more interest-on-interest is earned & therefore interest earned in Part (b) is more than twice of interest earned in Part (a).

e) Simple Interest for Part (a) = 4000*6%*3 = $720. Interest-on-interest earned = $764.06 - $720 = $44.06. Simple interest for Part (b) = 4000*6%*6 = $1,440. Interest-on-interest earned = $1,674 - $1,440 = $234.08