Chapter E, Problem 1SSQ

To determine

Calculate the future value for the given items.

Explanation of Solution

Future value:

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

Annuity:

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

a. 1

Calculate the future value of $50,000 deposited in the savings account for 10 years, annual interest rate of 12 % compounded annually.

$\begin{array}{c}\text{Future value of the amount deposited = }\left(\begin{array}{l}\text{Amount deposited }\times \\ \text{Future value factor for 10 years at 12 \% interest}\end{array}\right)\\ =\$50,000\times 3.106\\ =\$155,300\end{array}$

Therefore, the future value of the amount deposited is $155,300.

a. 2

Calculate the future value of $50,000 deposited in the savings account for 10 years, annual interest rate of 12 % compounded semiannually.

$\begin{array}{c}\text{Future value of the amount deposited = }\left(\begin{array}{l}\text{Amount deposited }\times \\ \text{Future value factor for 10 years at 12 \% interest}\end{array}\right)\\ =\$50,000\times 3.207\\ =\$160,350\end{array}$

Therefore, the future value of the amount deposited is $160,350.

Note:

When future value is compounded semiannually, the number of years will be doubled and the rate of interest will decrease by half of the given interest rate.

a. 3

Calculate the future value of $50,000 deposited in the savings account for 10 years, annual interest rate of 12 % compounded quarterly.

$\begin{array}{c}\text{Future value of the amount deposited = }\left(\begin{array}{l}\text{Amount deposited }\times \\ \text{Future value factor for 10 years at 12 \% interest}\end{array}\right)\\ =\$50,000\times 3.262\\ =\$163,100\end{array}$

Therefore, the future value of the amount deposited is $163,100.

b.

Calculate the future value of $5,000 amount received at the end of each year for 10 years, if the money earns an interest at the rate of 4% compounded annually.

$\begin{array}{c}\begin{array}{l}\text{Future value of the}\\ \text{ amount deposited}\end{array}\}\text{ = }\left(\begin{array}{l}\text{Amount deposited }\times \\ \text{Future value of annuity factor for 10 years at 4 \% interest}\end{array}\right)\\ =\$5,000\times 12.006\\ =\$60,030\end{array}$

Therefore, the future value of the amount deposited is $60,030.

c.

Calculate the future value of $3,000 amount received semiannually for the next five years, if the money earns an interest at the rate of 8% compounded semiannually.

 $\begin{array}{c}\begin{array}{l}\text{Future value of the}\\ \text{ amount deposited}\end{array}\}\text{ = }\left(\begin{array}{l}\text{Amount deposited }\times \\ \text{Future value of annuity factor for 10 years at 4 \% interest}\end{array}\right)\\ =\$3,000\times 12.006\\ =\$36,018\end{array}$

Therefore, the future value of the amount deposited is $36,018.

Note:

When future value is compounded semiannually, the number of years will be doubled and the rate of interest will decrease by half of the given interest rate.

d.

Calculate the future value of $1,000 amount deposited each year for the next 10 year, if the annual interest at the rate of 10% compounded annually.

$\begin{array}{c}\begin{array}{l}\text{Future value of the}\\ \text{ amount deposited}\end{array}\}\text{ = }\left(\begin{array}{l}\text{Amount deposited }\times \\ \text{Future value of annuity factor for 10 years at 10 \% interest}\end{array}\right)\\ =\$1,000\times 15.937\\ =\$15,937\end{array}$

Calculate the future value of $15,000 deposited today, with the annual interest at the rate of 10% compounded annually.

$\begin{array}{c}\begin{array}{l}\text{Future value of the}\\ \text{ amount deposited}\end{array}\}\text{ = }\left(\begin{array}{l}\text{Amount deposited }\times \\ \text{Future value factor for 10 years at 10 \% interest}\end{array}\right)\\ =\$15,000\times 2.594\\ =\$38,910\end{array}$

Therefore, the future value of the amount deposited is  $\left[\$15,937+\$38,910\right]$ $54,874.