Question

Suppose a relative has promised to give you $1,000 as a wedding gift the day you get engaged. Assuming a constant interest rate of 7%, consider the present and future values of this gift, depending on when you become engaged.
Complete the first row of the table by determining the value of the gift in one and two years if you become engaged today.

Present Value Value in One Year Value in Two Years
Date Received (Dollars) (Dollars) (Dollars)
Today 1,000.00 ? ?
In 1 year ? 1,000.00
In 2 years ? 1,000.00

Complete the first column of the table by computing the present value of the gift if you get engaged in one year or two years.

The present value of the gift is __________ if you get engaged in two years than it is if you get engaged in one year.

Answer 1

Answer:

a.

Future Value in One Year = $1,070.00

Future Value in Two Years = $1,144.90  

b.

Present Value of amount received in 1 year = $934.58  

Present Value of amount received in 2 years = $873.44

The present value of the gift is less/lower if you get engaged in two years than it is if you get engaged in one year.

Explanation:

These can be done as follows:

                            Present Value  Value in One Year   Value in Two Years

Date Received         (Dollars)             (Dollars)                      (Dollars)

Today                      1,000.00              1,070.00                       1,144.90

In 1 year                      934.58              1,000.00

In 2 years                   873.44                                                   1,000.00

a. Complete the first row of the table by determining the value of the gift in one and two years if you become engaged today.

To do this, we use future value (FV) formula as follows:

Future Value = A * (1 + r)^n ........................................ (1)

Where;

A = Amount received to day = $1,000.00

r = interest rate = 7%, or 0.07

n = number of years

Using equation (1), we therefore have:

Future Value in One Year = 1,000.00 * (1 + 0.07)^1 = $1,070.00

Future Value in Two Years = 1,000.00 * (1 + 0.07)^2 = $1,144.90  

b. Complete the first column of the table by computing the present value of the gift if you get engaged in one year or two years.

To do this, we use present value (PV) formula as follows:

Present Value = A / (1 + r)^n ........................................ (2)

Where;

A = Amount received in specified year = $1,000.00

r = interest rate = 7%, or 0.07

n = number of years

Using equation (2), we therefore have:

Present Value of amount received in 1 year = 1,000.00 / (1 + 0.07)^1 = $934.58  

Present Value of amount received in 2 years = 1,000.00 / (1 + 0.07)^2 = $873.44

Since $873.44 is less/lower than $934.58, we therefore have:

The present value of the gift is less/lower if you get engaged in two years than it is if you get engaged in one year.