Chapter 3, Problem 24P

To determine

(a)

The matured amount after $10$ years using formula.

Answer to Problem 24P

The matured amount after $10$ years using formula is $\$7012.04$.

Explanation of Solution

Given:

Interest rate is $2.4\%$.

Time period is $10$ years.

Calculation:

Write the expression to calculate the future value.

$F=P{\left(1+i\right)}^n$ ...... (I)

Here the present amount is, $P$, the future amount is $F$, the rate of interest is $i$ and the time period is $n$.

Substitute $0.024$ for $i$, $10$ for $n$ and $\$5530$ for $P$ in Equation (I).

$\begin{array}{c}F=\$5530{\left(1+0.024\right)}^{10}\\ =\$5530\left(1.268\right)\\ =\$7012.04\end{array}$ ...... (II).

Conclusion:

Therefore, the matured amount after $10$ years using formula is $\$7012.04$.

To determine

(b)

The matured amount after $10$ years using interest table and interpolation.

Answer to Problem 24P

The matured amount after years using interest table and interpolation is $\$7017.57$.

Explanation of Solution

Given:

Interest rate is $2.4\%$.

Time period is $10$ years.

Calculation:

Draw the table to calculate the future value at $2\%$ and $3\%$.

Year	P	Compound interest factor at $2\%$	Compound interest factor at $3\%$	Future amount at $2\%$ $d=\left(a_0\times b\right)$	Future amount at $3\%$ $e=\left(a_0\times c\right)$
$0$	$\$5530$
$10$		$1.219$	$1.344$	$\$6741.07$	$\$7432.32$

Here, factors are calculated by using Equation shown below.

$\text{Factor}={\left(1+i\right)}^n$.

Find the future value at $2.4\%$ using interpolation.

$\frac{x_2-x_1}{y_2-y_1}=\frac{x-x_1}{y-y_1}$ ........ (III)

Here, the higher value of future amount is $x_2$, and the lower value of future amount is $x_1$, the future value to be calculated is $x$, the higher interest rate is $y_2$, the lower interest rate is $y_1$ and the interest rate at which interpolation is to be done is $y$.

Substitute $\$7432.32$ for $x_2$, $\$6741.07$ for $x_1$, $3\%$ for $y_2$, and $2\%$ for $y_1$, and $2.4\%$ for

$y$ in Equation (III).

$\begin{array}{l}\frac{\$7432.32-\$6741.07}{0.03-0.02}=\frac{x-\$6741.07}{0.024-0.02}\\ \frac{\$691.25}{0.01}=\frac{x-\$6741.07}{0.004}\\ x=\$7017.57\end{array}$.

Conclusion:

Therefore, the matured amount after $10$ years using interest table and interpolation is $\$7017.57$.

To determine

(c)

The matured amount after $10$ years using spreadsheet.

Answer to Problem 24P

The matured amount after $10$ years using spreadsheet is $\$7010.11$.

Explanation of Solution

Given:

Interest rate is $2.4\%$.

Time period is $10$ years.

Calculation:

The spreadsheet for a $5$ button solution is shown below.

Conclusion:

Therefore, the matured amount after $10$ years using spreadsheet is $\$7010.11$.