2.2. Future Value
Future value is the value in Rands that an investment or series of investments will grow over a stated time period at a specified interest rate.
Definition
Future value is the value in Rands that an investment or series of investments will grow over a stated time period at a specified interest rate.
Simple interest is interest earned on the principal amount and it remains constant throughout the investment period.
Definition
Simple interest is interest earned on the principal amount and it remains constant throughout the investment period.
Compound interest on the other hand is additional interest that is earned if interest earned in the prior period is re-invested. Therefore, in each investment period the principal amount continues to increase thereby increasing the interest earned as well. The total amount of interest earned depends on the number of times interest is compounded.
Definition
Compound interest on the other hand is additional interest that is earned if interest earned in the prior period is re-invested
There is a direct relationship between the future value and interest earned with the number of times interest is compounded.
It often happens that an investment offers a rate of interest per annum, but stipulates that interest will be compounded at different intervals – quarterly or monthly for example. This means that interest is added more frequently than once a year. As a result, there is more opportunity for earning interest on interest. The net effect is that a higher return is obtained on the investment than would have been the case had interest only been compounded annually.
In such a case the quoted per annum rate is called the quoted rate while the true return in annual terms is higher if the number of compounding periods is more than once a year and is called the annual effective rate.
FV = PV(1+ rm)mn
where m = the number of times within a year that interest is compounded
n = the number of years
An investor deposits R100 into an account which offers 12% p.a. interest compounded monthly. Find the value of the investment at the end of one year.
Because interest is compounded monthly, it can be said that 12% over 12 months i.e., 1% interest is added every month.
FV = R100 (1.01)12 = R100 x 1.1268 = R112.68
The effective rate in this example is 12.68%
Using the information as above, find the value of the investment after 10 years.
FV = PV(1+ rm)mn = 100 (1+ 0.1212)12 x 10 = 100 x 1.01120 = 100 x 3.300
= R330
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It is useful to be able to convert a quoted or nominal interest rate into an effective interest rate for many reasons, particularly in order to compare investment alternatives with different compounding periods. We can accept that two interest rates are equivalent if they have the same effect, that is, if a single amount invested at one rate and compounded annually for a length of time accumulates to the same future value as another rate compounded more frequently.
The effective annual rate of interest is the annual rate that if compounded once a year would give us the same result as the interest per period compounded a number of times per year.
Definition
The effective annual rate of interest is the annual rate that if compounded once a year would give us the same result as the interest per period compounded a number of times per year
The future value of an investment earning interest at 6% per year, with interest compounded continuously, is determined by multiplying the present value by ern.
If we were investing R10 000 at 6% for 10 years with interest compounded continuously, what would the future value of the investment be?
Future Value = Present Value x 2.718280.06 x 10
= R10 000 x 1.822119 = R18 221.19
Alternatively, using the effective annual interest rate:
Future Value = R10 000 x 1.061836510
= R18 221.19