Question

Find the rate of interest required to achieve the conditions set forth:

A = $5000; P = $1250; t = 12 years; interest is compounded quarterly.

Answer 1

The Formula for the compound interest is:


`A=P(1+ (r)/(n))^(n*t)`

A = Amount Accumulated = $5000
P = Principal Amount = $1250
n = compound period in a year = 4
r = Interest Rate
t = Time in years = 12

Using the values in the formula, we get:


`5000=1250(1+ (r)/(4))^(4*12) \\ \\ (5000)/(1250) =(1+0.25r)^(48) \\ \\ 4=(1+0.25r)^(48) \\ \\ 1+0.25r=1.0293 \\ \\ 0.25r=0.0293 \\ \\ r=0.1172`

Thus, in order to achieve the given conditions, 11.72% interest rate is required.