Answer
Investment having an interest rate of 7% that is compounded monthly is better than the investment having an interest rate of 6.85% compounded continuously. The difference between the investments is $362 .
Work Step by Step
Calculation of future value of loan can be done with the mentioned formula:
\[A=P\times {{\left( 1+\frac{r}{n} \right)}^{nt}}\]
where A denotes the future value of the amount, P denotes the principal amount, r denotes the rate of interest, t denotes the number of years, and n denotes the number of times compounding is done in a year.
Compute the future value by substituting the values in the formula as mentioned below:
\[\begin{align}
& A=P\times {{\left( 1+\frac{r}{n} \right)}^{nt}} \\
& =\$14,000\times{{\left(1+\frac{0.07}{12}\right)}^{12\times10}}\\&=\$14,000\times{{\left(1+0.005833\right)}^{120}}\\&=\$28,134.24\end{align}\]
The future value of the amount when interest compounded monthly is \[\$28,135.24\].
Compute the future value of amount when interest is compounded continuously as mentioned below:
\[\begin{align}
& A=P\times {{e}^{rt}} \\
& =\$14,000\times{{2.71828}^{0.0685\times10}}\\&=\$27,772.79\end{align}\]
Computation of the difference in investment amount can be done by deducting the compounded continuously from the compounded monthly.
Compute the interest amount as mentioned below:
\[\begin{align}
& \text{Difference between the investment}=\text{compounded monthly}-\text{compounded continuously} \\
& =\$28,134.24-\$27,772.79\\&=\$361.5\\&\approx\$362\end{align}\]
Investment having an interest rate of 7% that is compounded monthly is better than the investment having an interest rate of 6.85% compounded continuously. Difference between the investments is \[\$362.\]
