Question

An investment with an original value of $11,000 is sold for proceeds of $12,950.00. if the investment yield was 5% compounded semi-annually, for how many yrs was the money invested?

Answer 1

Given:

Principal amount= $11000

Total amount = $12950

Rate = 5% compunded semi-annually.

The formula for compound interest is,

`\begin{gathered} A=P(1+(r)/(n))^{nt^{}} \\ A=12950,P=11000,r=5\text{ \%},n=2 \\ 12950=11000(1+(5)/(2*100))^(2t) \\ (12950)/(11000)=(1+0.025)^(2t) \\ (259)/(220)=1.025^(2t) \\ Apply\text{ exponent rule} \\ \ln ((259)/(220))=2t\ln (1.025) \\ t=(\ln ((259)/(220)))/(2\ln (1.025)) \\ t=3.305 \end{gathered}`

Answer: the amount is invested for 3.305 years . It is about 3 years 4 months.