12. The time value of money

Consider the following scenarios:

DelMonico Family

The DelMonicos have saved $5,000 towards their goal to have $45,000 for a down payment on a house in 6 years.

They will put the $5,000 in an account along with money they will deposit annually. They don’t know how much that annual deposit should be, so they’ve asked you to calculate it

They have found a savings institution that will pay 6% interest.

Decker Family

The Deckers have set a goal to have $45,000 for a down payment on a house in 6 years.

They have not saved anything so far.

They have asked you to calculate how much they will need to put away each year to achieve their $45,000 down-payment goal.

They have found a savings institution that will pay 6% interest.

Use the scenarios along with the following factor table data to answer each of the questions. Note that the complete Future Value and Future Value Annuity tables (as well as the Present Value and Present Value Annuity tables) are located in the appendix in your text.

Table of Future Value Factors:

	Interest Rate
Year	5%	6%	8%
1	1.050	1.060	1.080
2	1.102	1.120	1.166
3	1.158	1.190	1.260
4	1.216	1.260	1.360
5	1.276	1.340	1.469
6	1.340	1.420	1.587
8	1.477	1.590	1.851
10	1.629	1.790	2.159

Table of Future Value Annuity Factors:

	Interest Rate
Year	5%	6%	8%
1	1.000	1.000	1.000
2	2.050	2.060	2.080
3	3.152	3.180	3.246
4	4.310	4.380	4.506
5	5.526	5.630	5.867
6	6.802	6.970	7.336
8	9.549	9.890	10.637
10	12.578	13.180	14.487

What is the amount of money the DelMonicos will need to deposit annually (rounded to the nearest two decimal places) to achieve their down-payment goal?

$5,437.60

Points:

1 / 1

What is the amount of money the Deckers will need to deposit annually (rounded to the nearest two decimal places) to achieve their down-payment goal?

$6,456.24

To calculate the DelMonico annual deposit amount, you must first calculate the future value of the $5,000 they will be putting away now (at 6%). This is the amount their $5,000 will be worth in 6 years.

$5,000 x 1.420 = $7,100

This amount is subtracted from their down payment to determine the amount they still need to save to achieve their down-payment goal.

$45,000 – $7,100 = $37,900

This net amount is then divided by the future value of an annuity factor to determine the annual amount that must be added to their $5,000 to accumulate the funds that constitute their down-payment goal.

$37,900 / 6.970 = $5,437.59

The Decker calculation is simpler. Take their down-payment goal amount and divide it by the future value of an annuity factor.

$45,000 / 6.970 = $6,456.24

Note: The use of calculators or a spreadsheet application may result in a slightly different answer due to rounding.