Question

7. (a) Will the future value be larger or smaller if we compound an initial amount more often than annually--for example, every 6 months, or semiannually - holding the stated interest rate constant? Explain your answer. (b-1) What is the future value of $200 after three years under 12% semiannual compounding? (b-2) What is the effective annual rate for 12% interest with semiannual compounding? (C-1) What is the future value of $200 after three years under 12% quarterly compounding?) (c-2) What is the effective annual rate (EAR) for 12% interest with quarterly compounding?) (d-1) What is the future value of $200 after three years under 12% daily compounding? Assume 365 day years and do not do any interim rounding. Just enter the interest rate. divide by 365, hit "=" then hit your I/Y key (or similar for other calculators). (d-2) What is the effective annual rate for 12% interest with daily compounding?

Answer 1

As per rules I am answering the first 4 subparts of the question

a: The future value will be larger if compounding is more frequent. This is due to greater interest accumulated on interest earned. FV=PV*(1+r)^n. Hence greater the value of n greater will be the FV.

b-1: Future Value= PV*(1+r)^n

= 200*(1+12%/2)^(3*2)

= 283.70

b-2: EAR=(1+APR/m)^m -1

= (1+12%/2)^2-1

= 1.1236-1

=12.36%

c-1: Future Value= PV*(1+r)^n

= 200*(1+12%/4)^(3*4)

=$285.15