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 10%, 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.
te Received Present Value Value in One Year Value in Two Years
(Dollars) (Dollars) (Dollars)
Today 1,000.00 1) 2)
In 1 year 3) 1,000.00
In 2 years 4) 1,000.00
The present value of the gift is 5) (GREATER or SMALLER) if you get engaged in two years than it is if you get engaged in one year.

1. Value in One Year = Future value in one year = $1,100

2. Value in Two Year = Future value in two years  = $1,210

3. Present value of Value in One Year = $909.09

4. Present value of Value in Two Years = $826.45

Based on the above, the present value of the gift is 5) SMALLER if you get engaged in two years than it is if you get engaged in one year.

Explanation:

Given:

Date Received      Present Value   Value in One Year   Value in Two Years

                                   (Dollars)                    (Dollars)                   (Dollars)

Today                         1,000.00                1)                 2)

In 1 year                     3)                  1,000.00

In 2 years                  4)                                                  1,000.00

The present value of the gift is 5) (GREATER or SMALLER) if you get engaged in two years than it is if you get engaged in one year.

Let:

r = constant interest rate = 10%, or 0.10

n = number of years as the case may be

Therefore, we have:

Future value formula = Present value * (1 + r)^n ………………… (1)

Present value formula = Future value / (1 + r)^n

1. Value in One Year = Future value in one year = $1,000 * (1 + 0.10)^1 = $1,100

2. Value in Two Year = Future value in two years = $1,000 * (1 + 0.10)^2 = $1,210

3. Present value of Value in One Year = $1,000 / (1 + 0.10)^1 = $909.09

4. Present value of Value in Two Years = $1,000 / (1 + 0.10)^2 = $826.45

Based on the abov, the present value of the gift is 5) SMALLER if you get engaged in two years than it is if you get engaged in one year.