Janet Boyle intends to deposit $300 per year in a credit union for the next 10 y

Question

Janet Boyle intends to deposit $300 per year in a credit union for the next 10 years, and the credit union pays an annual interest rate of 8%.

a. Determine the future value that Janet will have at the end of 10 years, given that end-of- period deposits are made and no interest is withdrawn, if

(1) $300 is deposited annually and the credit union pays interest annually.

(2) $150 is deposited semiannually and the credit union pays interest semiannually.

(3) $75 is deposited quarterly and the credit union pays interest quarterly.

b.   Use your findings in part a to discuss the effect of more frequent deposits and compounding of interest on the future value of an annuity.

Explanation / Answer

II:

As the above calculation, it has been shown that more than compoudning results the more value i.e. if we compare annual compouding with halfyear/qtly/montly compouding it will always greater than with the annual compouding.

(a): Amount invested 300 Annualy rate 8% Time 10 year Future value of annuity Cash flow * {1+r)^n-1}/r 300 *(1+8%)^10-1)/8% 300 *((1.08)^10-1)/8% 4345.969 (b) amount invested 150 Rate of interest 4% half yearly Time 20 half yearly Future value of annuity Cash flow * {1+r)^n-1}/r 150 *(1+4%)^20-1)/4% 150 *((1.04)^20-1)/4% 4466.712 © amount invested 75 Rate of interest 2% Qtrly Time 40 Qtr Future value of annuity Cash flow * {1+r)^n-1}/r 75 *(1+2%)^40-1)/2% 75 *((1.02)^40-1)/2% 4530.149

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