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

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

A = Amount Accumulated = $5000

P = Principal Amount = $1250

n = compound period in a year = 4

r = Interest Rate

t = Time in years = 12

$5000=1250({1+\frac{r}{4}})^{4\times 12}\\\frac{5000}{1250}=(1+0.25r)^{48}\\4=(1+0.25r)^{48}\\1.025r=1.0293\\0.25r=0.0293\\r=0.1172\\0.1172\times100=11.72\%$

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