Question

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

Answer 1

The Formula for the compound interest is:

$A=P(1+ \frac{r}{n})^{n*t}$

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:

$5000=1250(1+ \frac{r}{4})^{4*12} \\ \\ \frac{5000}{1250} =(1+0.25r)^{48} \\ \\ 4=(1+0.25r)^{48} \\ \\ 1+0.25r=1.0293 \\ \\ 0.25r=0.0293 \\ \\ r=0.1172$

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