Question

Find the interest rate for a 9000 deposit accumulating to 9883, compounded annually for 8 yearsThe interest rate is ____%

Answer 1

Given:

A 9000 deposit accumulates to 9883, compounded annually for 8 years.

So, P = 9000, A = 9883, t = 8 years, n = 1

We will find the interest rate = r

We will use the following formula:

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

Substitute the given values:

$9883=9000(1+\frac{r}{1})^{1*8}$

Solve the equation to find (r):

$\begin{gathered} (1+r)^8=\frac{9883}{9000} \\ \\ 8*ln(1+r)=ln(\frac{9883}{9000})\approx0.09359 \\ \\ ln(1+r)=\frac{0.09359}{8}\approx0.0116989 \\ \\ 1+r=e^^{0.0116989}\approx1.011767 \\ \\ r=1.0117676-1=0.0117676 \\ \\ r=1.17676\% \end{gathered}$

So, the answer will be:

The interest rate is 1.17676%