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Future Value of Single / Multiple Cash Flows

Assignment / Homework Help
To find out the future value of cash flows, we have to apply the compounding technique. Compounding may be yearly, half-yearly, quarterly, monthly etc.

Future Value of Single Cash Flow

Future value can be computed by the following formula:
FVn = PV (1 + r)n
Where
FV = Future value
PV = Present value
r = Rate of Interest
n = Number of periods

Example: FV of single cash flow compounded annually

Let us calculate the future value of an investment of $ 2,000 compounded annually at the rate of 12%, after 4 years period.

FV = $ 2,000 x (1 + 0.12) 4
= $ 3,147.04

Frequent Compounding:

Interest is compounded often more than once a year. In such cases, the formula for FV becomes:
In this case, the formula for FV becomes:

FVn = PV (1 + (r / m))n x m

Where:
m = Number of total compounding periods in a year
If compounded semi-annually, m=2
If compounded quarterly, m = 4 and so on. The more frequent compounding occurs in a year, the more would be the future value as illustrated below.


Example: FV of single cash flow compounded semi-annually

In the above example, let us assume that the interest of 12% is compounded semi-annually; rest of details being the same, the future value after 4 years would be:

Here:

m = 2
FV = $ 2,000 x (1 + (0.12 / 2)) 4 x 2
FV = $ 3,187.70

Thus, when interest is compounded yearly once, the FV is only $3,147.04 whereas if it is compounded twice a year, the FV is $3,187.70. Similarly, if interest is compounded quarterly or monthly, FV would accordingly be greater.

Future value using Simple Interest
If no interest is earned on the interest on the investment, it is called as simple interest. The future value of an investment in such cases would be calculated by the following formula:

FVn = PV (1 + [n x r])
Where
n = Number of years
r = Interest Rate

The future value using a simple interest would obviously be lower than the future value using compound interest as there is no interest earned on the interest portion of the investment.


Example:

An investment of $10,000, if invested at 13% simple interest rate will in 6 years be:

FV = $ 10,000 x (1 + [6 X 0.13])
FV = $ 17,800

Future Value of Multiple Cash Flows

In many instances, we may be interested in the future value of series of payments of different amounts at different time periods. In such cases, we can find the FV as illustrated below:

Example:

A person deposits $1000, $2000, $3000, $4000 and $5000 at the end of each of the 5 respective years. The interest rate is 10%, compounded annually. Find the future value.

End of Year Amount Deposited No. of years compounded Compounded Interest factor Future Value
(B x D)
A B C D E
 1 $ 1,000 1.4641 $ 1,464.10
 2 $ 2,000 1.331 $ 2,662.00
 3 $ 3,000 1.21 $ 3,630.00
 4 $ 4,000 1.1 $ 4,400.00
 5 $ 5,000 1.0 $ 5,000.00
TOTAL $ 17,156.10

The compounded interest factor is calculated as given below:

For 4 years = (1 + 0.10)4 = 1.4641
For 3 years = (1 + 0.10)3 =1.331 and so on...

Chart showing growth of individual deposited amounts from years 1 to 5
Assignment / Homework Help
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