Answer
See below
Work Step by Step
(a)
Calculation of future value of down payment can be done with the mentioned formula:
\[A=\frac{P\left[ {{\left( 1+\frac{r}{n} \right)}^{nt}}-1 \right]}{\left( \frac{r}{n} \right)}\]
Where A denotes the Future value of the loan, 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:
\[\begin{align}
& A=\frac{P\left[ {{\left( 1+\frac{r}{n} \right)}^{nt}}-1 \right]}{\left( \frac{r}{n} \right)} \\
& =\frac{\$100\left[{{\left(1+\frac{0.065}{12}\right)}^{12\times5}}-1\right]}{\left(\frac{0.065}{12}\right)}\\&=\frac{\$100\left[{{\left(1+.0054\right)}^{60}}-1\right]}{0.0054}\\&=\$7,067\end{align}\]
Hence, the value of down payment at the end of 5 years is\[\$7,067\].
(b)
Computation of the interest amount can be done by deducting the Principal amount (P) from the future value (A) of the loan. Compute the interest amount as mentioned below:
\[\begin{align}
& \text{Amount of interest}=\text{Value of down payment after 5 years}-\text{Amount deposited in 5 years} \\
& =\$7,067-\left(12\times5\times\$100\right)\\&=\$7,067-\$6,000\\&=\$1,067\end{align}\]
Hence, the amount of interest at the end of 5 years is\[\$1,067\].
(c)
The interest earned on this annuity is less than the interest earned from the lump-sum deposit because of only a part of $6,000 in invested in the installment deposit for the entire time period of 5 years.
Even when annuity gives less amount of interest on the deposit it is preferable as payment is made in installments.
