Chapter F, Problem 1E

a.

To determine

Calculate the future value of $30,000 invested at 8% for 10 years.

Explanation of Solution

Future value:

The future value is value of present amount compounded at an interest rate until a particular future date.

Calculate the future value of $30,000 invested at 8% for 10 years.

$\begin{array}{c}\text{Future value of amount invested = }\left(\begin{array}{l}\text{Future value factor of single }\\ \text{ payment at 8\% for 10 years}\end{array}\right)\times \text{Amount}\\ \text{=2}\text{.158925}\times \text{\$30,000}\\ \text{=\$64,768}\end{array}$

Therefore, the future value of the amount invested is $64,768.

b.

To determine

Calculate the future value of eight annual payments of $2,000 at 9% interest.

Explanation of Solution

Calculate the future value of eight annual payments of $2,000 at 9% interest.

$\begin{array}{c}\text{Future value of annuity}\}\text{= }\left(\begin{array}{l}\text{Future value factor of annuity }\\ \text{ payment for 8 years at 9\%}\end{array}\right)\times \text{Amount}\\ \text{=11}\text{.028474}\times \text{\$2,000}\\ \text{=\$22,057}\end{array}$

Therefore, the future value annuity is $22,057.

c.

To determine

Calculate the amount that must be deposited today at 8% to accumulate $60,000 in five years.

Explanation of Solution

Present value:

Present value is the current value of an amount that is to be paid or received in future. Present value is determined by using the formula:

$\text{Present Value = }\frac{1}{{\left(1+\text{i}\right)}^{\text{n}}}\times \text{Amount}$

Calculate the amount that must be deposited today at 8% to accumulate $60,000 in five years.

$\begin{array}{c}\text{Present value = }\left(\begin{array}{l}\text{Present value factor of the single }\\ \text{payment at 8\% for 5years}\end{array}\right)\times \text{Amount}\\ \text{=0}\text{.680583}\times \text{\$60,000}\\ \text{=\$40,835}\end{array}$

Therefore, the amount that must be deposited today at 8% to accumulate $60,000 in five years is $40,835.

d.

To determine

Calculate the annual payment on a 10 year, 6 percent, $50,000 note payable.

Explanation of Solution

Present value:

Present value is the current value of an amount that is to be paid or received in future. Present value is determined by using the formula:

$\text{Present Value = }\frac{1}{{\left(1+\text{i}\right)}^{\text{n}}}\times \text{Amount}$

Annuity:

An annuity is referred as a sequence of payment of fixed amount of cash flows that occurs over the equal intervals of time.

Calculate the annual payment on a 10 year, 6 percent, $50,000 note payable.

$\begin{array}{c}\text{Present value of annuity payment =}\frac{\text{Notes}\text{payable}}{\left(\text{Present value factor of annuity for 10 years at 6\% }\right)}\\ \text{=}\frac{\$50,000}{7.360087}\\ \text{=\$6,793}\end{array}$

Therefore, the annual payment on a 10 year, 6 percent, $50,000 note payable is $6,793.