Question

Find the annual rate of interest.Principal = 4600 rupeesPeriod5 yearsTotal amount =6440 rupeesAnnual rate of interest =%Stuck? Review related articles/videos or use a hint.

Answer 1

The compound interest is given, in general, by the next formula:

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

Where A is the amount, P is the initial amount, r is the rate of interest, n is the number of times the interest rate is applied in a period, and t is the numbers of periods.

Then, in our problem:

$A=6440,P=4600,t=5,n=1$

Solving the formula for r:

$\begin{gathered} n=1 \\ \Rightarrow A=P(1+r)^t \\ \Rightarrow(1+r)^t=\frac{A}{P} \\ \Rightarrow r=-1+\sqrt[t]{\frac{A}{P}} \end{gathered}$

Then, using the numerical values above:

$r=-1+\sqrt[5]{\frac{6440}{4600}}=-1+\sqrt[5]{\frac{7}{5}}\approx-1+1.0696\approx0.07$

Then, the rate of interest is approximately equal to 7%