Question

Yoko deposited $5000 into an account with a 5% annual interest rate, compounded semi annually. Assuming that no withdrawals are made, how long will it take for the investment to grow to $10,230? Do not round any intermediate computations, and round your answer to the nearest hundredths.

Answer 1

To solve this question, we need to use the formula of compound interest

`\begin{gathered} A=p(1+(r)/(n))^(nt) \\ A=10,230 \\ p=5000 \\ r=5\text{ \%=0.05} \\ n=2 \\ t=\text{ ?} \end{gathered}`

We would have to input these values into the above equation and solve for t

`\begin{gathered} a=p(1+(r)/(n))^(nt) \\ 10230=5000(1+(0.05)/(2))^(2* t) \\ (10230)/(5000)=(1+0.025)^(2t) \\ 2.046=1.025^(2t) \\ \text{Take the log of both sides} \\ \log 2.046=\log 1.025^{2t^{}} \\ \log 2.046=2t\log 1.025 \\ 2t=(\log 2.046)/(\log 1.025) \\ 2t=28.99 \\ (2t)/(2)=(28.99)/(2) \\ t=14.5 \end{gathered}`

It will take 14 years and 6 months for $5000 compounded annually at 5% to get to $10,230