Question

Suppose you invest $10,000 into a fund paying 3.6% annual interest. How much will you have after 5 years is the interest is compounded:

a) Annually

b) Semi-Annually

c) Quarterly

d) Monthly

Answer 1

Formula :

A = P(1 + r/n)^tn

where A = amount after n years that we have to calculate, P = principle invested = 10,000, r = annual interest rate = 3.6% = 0.036, n = number of compoundings in a year and t = time period in years = 5

(a) Annually

For annually, n = 1

=> A = P(1 + r/n)^tn = 10,000(1 + 0.036/1)^5*1 = 11934.35

Thus after 5 years you will have $11934.35

(b) Semi annually

For semiannually, n = 2(Because it is compounded after every 6 months and thus there will be 2 compoundings in a year)

=> A = P(1 + r/n)^tn = 10,000(1 + 0.036/2)^5*2 = 11953.02

Thus after 5 years you will have $11953.02

(c) Quarterly

For Quarterly, n = 4(Because it is compounded after every 3 months and thus there will be 4 compoundings in a year)

=> A = P(1 + r/n)^tn = 10,000(1 + 0.036/4)^5*4 = 11962.54

Thus after 5 years you will have $11962.54

(d) Monthly

For Monthly, n = 12(Because it is compounded after every 1 month and thus there will be 12 compoundings in a year)

=> A = P(1 + r/n)^tn = 10,000(1 + 0.036/12)^5*12 = 11968.95

Thus after 5 years you will have $11968.95