How FVIF formula Works

A dollar today is worth more than a dollar tomorrow. This is the core principle in the TIME-VALUE concept of money. The hidden meaning in the principle is that "A dollar today can earn some amount by tomorrow". This some amount may be interest, dividend or something else.

Does $100 is equal with the same $100 after 1 year ? Obviously not. So, what $100 today is worth after 1 year ? or what is the value of $100 after year at present ? These sort of questions are solved with TIME-VALUE concept of money in Finance.

In the table above, suppose Bimal invested Rs 100 today at 5% annual interest to be compounded annually. At the beginning or at year 0 (TODAY), he invested Rs. 100 @ 5% PA. At the end of year 0, or say beginning of Year 1 (simply after 365 days or a year later), he will earn Rs 5 as interest. In the next year (year 1), the interest will also earn interest. This is where the normal formula of simple interest fails .

In year 1, total interest is obvious more than that of year 0 because Rs 5 will also earn certain interest. Hence, the total amount earning interest for the ear is 105 (Rs. 100 + Rs 5). This is what we call CAPITALIZATION in time value concept.

calculating the interest manually is quite tedious. So finance scholars have developed formula for this. The base of this formula is obviously the concept told above.

We have the following in general
We have Rs. 100 today (PV = Rs. 100)
We invest it at 5% PA (i = 5% = 0.05)
We invest it for 5 years (n = 5yrs)
Value after 5 years (FV5) = ?

Note : Students when count from 0 to 5 in the table / graph above, they might get confused whether it is invested for 5 years or 6 ? To eliminate this, we can suggest you as Count 0 TO 1 as year 1, 1 TO 2 as year 2 and so on. Because Year 0 to year 1 is the first year that will earn interest, isn't it ?

Now, we have

FVn = PV0*FVIFi%, n yrs
FV5 = PV0 * FVIF 5%, 5 yrs
FV5 = 100 * FVIF5%, 5 yrs
FV5 = 100 * 1.2763
FV5 = 127.63

FV = PV * FVIF i%, n Yrs

FV = PV * (1 + i )ⁿ

Note : i = i%/100 (5% = .05)

FVIF i%, n Yrs = (1 + i )ⁿ

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