Question

. What happens to future values as the length of time involved increases?   What happens to present values as the length of time involved increases?

Answer 1

Formula for Future value (FV) is,

FV = PV x (1 + r)ⁿ

Formula for Present value (PV) is,

PV = FV/(1+r)ⁿ

Where, r is the rate of discount and n is the number of periods.

If length of the time increases, the value of n increases which results in the increase in interest amount.

Future value will increase on increasing interest portion as it is multiplied with PV to get FV.

On the other hand present value will decrease on increasing interest portion which divides to FV to get PV.

We can illustrate by considering below examples.

Let’s calculate FV and PV of $ 1,000 @ 10 % with different time periods.

For n = 5;

FV = $ 1,000 x (1+0.1)⁵ = $ 1,000 x (1.1)⁵ = $ 1,000 x 1.61051 = $ 1610.51

PV = $ 1,000 / (1+0.1)⁵ = $ 1,000 / (1.1)⁵ = $ 1,000 / 1.61051 = $ 620.92

For n = 10;

FV = $ 1,000 x (1+0.1)¹⁰ = $ 1,000 x (1.1)¹⁰ = $ 1,000 x 2.593742 = $ 2593.74

PV = $ 1,000 / (1+0.1)¹⁰ = $ 1,000 / (1.1)¹⁰ = $ 1,000 / 1.61051 = $ 385.54

As the time period increased FV increased and PV decreased as per above discussion.