Question

Future and present values 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 wift, depending on when you become engaged. 

Complete the first row of the following table by determining the value of the gift in one and two years with interest if you become engaged today and save the money.

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

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

Answer 1

The table is computed below

Date received	Present value	Value in 1 year	Value in 2 year
Today	1000	1070	1144.90
Year 1	934.58	1000	1070
Year 2	873.44	934.58	1000

The Present value of 1000 today is 1000 today but will become 1000 x 1.07^1 = 1070 1 year from now and 1000 x 1.07^2 = 1144.90 2 years from now.

The Present value of 1000 one year from now is 1000*1.07^-1 = 934.58 today but will become 934.58 x 1.07^1 = 1000 1 year from now and 934.58 x 1.07^2 = 1070 2 years from now

The Present value of 1000 two years from now is 1000*1.07^-2 = 873.44 today but will become 873.44 x 1.07^2 = 934.58 1 year from now and 873.44 x 1.07^2 = 1000 2 years from now

The present value of gift is low if you engage in two years than in one year.

Answer 2

Solution:

The prevailing interest rate is 5%

We assume that the money is compounded, that is, the interest also earns interest.

We know that,

A = P × (1+i)?

Where n = Number of years of compounding

P = Principle amount

i = rate of interest = 5%

Also, P = A / (1+i)

If we receive $1000 today,

The value in one year will be :

1000 × (1+0.05) = $1050.

(note: accumulating for one year)

The value in two years will be :

1000 × (1+i)² = $1102.5

(note : accumulating for two years )

Similarly,

If we receive $1000 in one year,

Its value now will be:

$1000 / (1+0.05) = $952.381

(note : discounting for one year)

Its value in 2 years will be :

1000 × (1+0.05) = $1050

(note : accumulating for one year)

Again, if we get the money in 2 years,

Its value at time 1 will be :

1000 / (1+0.05) = $952.381

(note discounting for 1 year)

Ita value at time today will be :

1000 / (1+0.05)² = $907.0295

(note : discounting for 2 years)

Present value = value of the gift today :

If one gets married in 1 year,

The value today (at time 0) will be $952.381 [as calculated above]

And if one gets married in 2 years,

The value now (at time 0) will be $907.0295

Thus, the present value of the gift is greater if one gets engaged in 1 year that if he gets engaged in the 2 years.