Question

Elijah invested $610 in an account paying an interest rate of 4.1% compoundedannually. Assuming no deposits or withdrawals are made, how long would it take, to the nearest year, for the value of the account to reach $900?

Answer 1

Use the formula for the compounding of interest

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

since the compounding is annually, n=1 which reduces the formula to

$A=p(1+r)^t$

use values for

A=900

p=610

r=0.041

solve the equation for t

$900=610\cdot(1+0.041)^t$$\frac{900}{610}=(1.041)^t$$\ln (\frac{900}{610})=\ln (1.041)^t$

apply the log properties

$\ln (\frac{900}{610})=t\cdot\ln (1.041)$

solve for t

$\begin{gathered} t=\frac{\ln (\frac{900}{610})}{\ln (1.041)} \\ t\approx9.68 \end{gathered}$

It would take about 10 years to reach 900 in the account