Question

There are important relationships between Interest Rates and Time as it relates to Future Value:

1. For a given Interest Rate, what is the impact on Future Value if the Time Period is longer and for a given Time Period, what is the impact on Future Value if the Interest Rate is higher?

Answer 1

Future value = Present value x (1+ Interest rate)^{Number of periods}

If time period is longer i.e. on increasing number of periods, keeping PV and interest rate constant, the interest term or second term increase resulting in increasing in future value.

We can consider an example,

PV = $ 1,000; rate = 0.05, Number of periods = 10

FV = $ 1,000 x (1+0.05)¹⁰

= $ 1,000 x (1.05)¹⁰

= $ 1,000 x 1.628894627

= $ 1,628.89

If number of periods = 12,

FV = $ 1,000 x (1.05)¹²

  = $ 1,000 x 1.795856326

   =$ 1,795.86

Future value increased if time of investment is longer.

Let’s increase the interest rate for the above example and see the consequence:

Periodic interest rate = 0.08

FV = $ 1,000 x (1.08)¹⁰

=$ 1,000 x 2.158924997

= $ 2,158.92

Future value increased if interest rate of investment is higher, keeping amount and time of investment unchanged.

Hence it is concluded that future value is directly related to time period and interest rate.

On increasing any one or both of these two parameters, future value increases for same present amount.