Question

Do not round intermediate computations, and round your answer to the nearest hunderdth

Answer 1

Given:

Principal = $2500

Rate = 7.5% per annum (compounded monthly)

Amount needed to constitute: $3000

To find:

Number of years

Step by step solution:

$\begin{gathered} \text{ }A=p(1+\frac{r}{(100)(12)})^{12n} \\ \\ 3000=2500(1+\frac{7.5}{(100)(12)})^{12n} \\ \\ 1.2=(1.00625)^{12n} \\ \\ 1.2=(1.00625)^{12n} \\ \end{gathered}$

We will use logarithm to solve the question furtherly:

$\begin{gathered} ln(1.2)=12n[ln(1.00625)] \\ \\ n=\frac{ln(1.2)}{12ln[1.00625]} \\ \\ n=\text{ 2.439 years} \end{gathered}$

We can take it's value to approx 2 years 5 months.