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))`

`(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.

`(0.9645)/(10)=r`

`0.09645=r`

The rate of interest in percentage is:

`r=100* 0.09645`

`r=9.645\%`

Therefore, the required rate of interest is 9.645%.