If an amount of money is subject to a rate of interest, it will grow over time. Thus, the value of the amount of money changes over time. This change is known as the time value of money. For example, if $1000 is invested today at 4% p.a. simple interest. In three months, this value is $1010, $1020 in six months, and $1040 in one year.
The value $1000 today, $1010 in three months, $1040 in one year are called equivalent values as they represent the same investment with the same interest rate at different times.
This is important because in order to compare choices, we must make a rational choice on a specific date called the focal date. The focal date can be set on any date.
The choice of calculating the Present Value, P, compared to the Future Value, S, depends on the relation of the due date/payment date in comparison to the focal date.
1. If the due date falls before the focal date, calculate the future value, S.This means with a positive interest rate, you should get a larger value after calculation. For simple interest, you will be calculating S from \(S=P(1+rt)\).
2. If the due date falls after the focal date, calculate the present value, P.This means with a positive interest rate, you should get a smaller value after calculation. For simple interest, you will be calculating P from \(P=\frac{S}{1+rt}\).
Example
On March 1, Bear Mountain Tours borrowed $1500. Three equal payments are required, on April 30, June 20, and August 10, as well as final payment of $400 on September 30 of the same year. If the focal date is September 30, what is the amount of the equal payments at 6.75%?
Solution
See the video below to see how to solve this problem.
