Question

An amount is invested at 8%, compounded quarterly, for 2 years. What rate and what number of periods would be used to find a future value factor from the tables in order to calculate the future value of this investment?

a)2% for 4 periods	b) 8% for 2 periods
c)2% for 8 periods	d)8% for 4 periods

An investment earning 12% interest compounded semi-annually, will accumulate to a greater amount in the future than an equal investment earning 12% compounded quarterly (assume that the two alternatives would be invested for the same amount of time). - True or False?

Answer 1

Answer for Question 1 : (c) 2% for 8 periods

Note : While computing compounding interest quarterly, then interest rate percent should be divided by 4(3 months ie 4 times in a year) and number of years is multiplied by 4.

Hence, Rate of interest per unit time = r / 4 = 8% / 4 = 2%

Number of units of time = 4 n = 4 x 2 = 8 periods

Answer for Question 2 : False

An investment earning 12% interest compounded quarterly will accumulate to greater amount in the future than an equal investment earning 12% compounded semi annually.

If amount,(P) = $ 1,00,000 number of years,(n) = 5 interest rate(r) = 12%

Future value = P(1+r)ⁿ

Option 1 Semi Annually = $ 1,00,000 x (1.06)¹⁰ = $ 1,00,000 x 1.7908 = $ 1,79,080

Option 2 Quarterly = $ 1,00,000 x (1.03)²⁰ = $ 1,00,000 x 1.8061 = $ 1,80,610

Hence interest compounded quarterly provide more earnings than compounded semi annually.