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

Explanation:

`\mathrm{Compound \ Interest \ Formula}\\$$\begin{aligned}&A=p\left(1+(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+(8)/(100)\right)^(1 . t) \\453.60=420\left((108)/(100)\right)^(t) \\(453.60)/(420)=\left((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