Question

a company lends $1,400,000 for 1 years at 12%, compounded monthly to another company that manufacturers tug boats. find the future value and the interest? Simplify your answer for both

Answer 1

We are provided with the following, from the question:

$\begin{gathered} Total\text{ amount: \ 1,400,000} \\ Interest\text{ rate:12\%} \\ \text{Time:}1\text{year} \end{gathered}$

The future value can be obtained using the formula:

$\begin{gathered} FV=PV(1+r)^n \\ PV\colon\text{present value} \\ r\colon annual\text{ interest rate} \\ n\colon number\text{ of periods interest held} \end{gathered}$

Thus, we have:

$\begin{gathered} FV=1,400,000(1+\frac{12\text{\%}}{12})^{1\times12} \\ FV=1,400,000(1+0.01)^{12} \\ FV=1,400,000(1.01)^{12} \\ FV=1,400,000(1.126825) \\ FV=\text{ \ }1,577,555.042 \\ FV=\text{ \ 1,577,555 (to the nearest whole number)} \end{gathered}$

To get the interest, we have:

$\begin{gathered} \text{Interest}=FV-PV \\ \text{Interest}=1,577,555.042-1,400,000 \\ \text{Interest}=\text{ \ }177,555.042 \\ \text{Interest}=\text{ \ 177,555 (to the nearest whole number)} \end{gathered}$