Question

Katelyn invested $1500 into her account which earned interest compounded continuously. After 10 years, she discovered that she had $3935.36. What interest rate percent did Katelyn earn?

Answer: ____ % interest

Answer 1

Given:

Principal = $1500

Time = 10 year

Amount after interest compounded continuously = $3935.36

To find:

The rate of interest.

Solution:

The formula for amount after continuous compound interest is:

$A=Pe^{rt}$

Where, P is principal, r is the rate of interest in decimal and t is time in years.

Putting $P=1500,A=3935.36,t=10$ in the above formula, we get

$3935.36=1500e^{r(10)}$

$\dfrac{3935.36}{1500}=e^{10r}$

$2.6236=e^{10r}$

Taking ln on both sides, we get

$\ln(2.6236)=\ln e^{10r}$

$0.9645=10r$                   $[\because \ln e^x=x]$

Divide both sides by 10.

$\dfrac{0.9645}{10}=r$

$0.09645=r$

The rate of interest in percentage is:

$r=100\times 0.09645$

$r=9.645\%$

Therefore, the required rate of interest is 9.645%.