Question

How much money do you have to put into a bank account that pays 10% interest compounded annually to have $10,000 in ten years?

Short answer

Money to be put in bank is$\$3856.53$.

Step-by-step solution

Concept Introduction

Compound interest : It is the addition of interest to the principal sum of loan.

Explanation of Solution

Given : $\mathrm{A}=\$10,000,\mathrm{n}=10\text{years,}\mathrm{r}=10\%,\mathrm{p}=?$

Using compound interest formulae,

$A=P{\left(1+\frac{r}{100}\right)}^n$

$\$10,000=P{\left(1+\frac{10}{100}\right)}^{10}$

$\$10,000=P(1+0.1{)}^{10}$

$\$10,000=P(1.1{)}^{10}$

$\$10,000=P(2.593)$

$P=\frac{10,000}{2.593}$

$=3856.53$

Hence, principal is $\$3856.53$.