Question

1. Time value of money
   1. How many years your money will be doubled by using the compounded interest method if the interest rate is 8%?
   2. How many years your money will be doubled by using the simple interest method if the interest rate is 8%?
   3. Did your answer for a and b different? Why?

Answer 1

a]

future value = present value * (1 + r)^t

where r = rate of interest

t = number of years

$2 = $1 * (1 + 8%)^t

1.08^t = 2

t = log_1.082

t = 9.01

It will take 9.01 years for the money to double

b]

future value = present value * (1 + rt)

where r = rate of interest

t = number of years

$2 = $1 * (1 + 0.08t)

t = 1 / 0.08

t = 12.50

It will take 12.50 years for the money to double

c]

The answer is lower for part (a) because part (a) is compounded interest.

With compound interest, the interest in each year is added to the original investment, and the interest in each subsequent years is calculated on the increased amount. Thus, interest is earned on interest as well. This is not the case with simple interest, where interest in each year is calculated only on the original principal. Thus, the time taken for the money to double is lower with compound interest