Question

4. You put $420 into a savings account with an interest rate of 8% compounded annually which earns $33.60 over a period of time. How long was the period of time?


(how to find compound interest time)​

Answer 1

Answer: 1 year

Step-by-step explanation:

$\mathrm{Compound \ Interest \ Formula}\\ \begin{aligned}&A=p\left(1+\frac{r}{n}\right)^{n t} \\&A=420+33.60=\ 453.60 \\&p=\ 420 \\&r=8 \% \\&n=1\end{aligned}$

$\mathrm{Solving \ for \ t:}$

$\begin{gathered}453.60=420\left(1+\frac{8}{100}\right)^{1 . t} \\453.60=420\left(\frac{108}{100}\right)^{t} \\\frac{453.60}{420}=\left(\frac{108}{100}\right)^{t} \\1.08=(1.08)^{t}\end{gathered}$

$\mathrm{Taking \ log \ of \ both \ sides}\\\log 1.08=\log (1.08)^{t} \\\log 1.28=t \log (1.08) \\1=t \\ t=1$

Therefore, the period of time taken to earn $33.60 was 1 year