The IF for the future value of an annuity is 4.5 at 10% for 4 years. If we wish to accumulate 8,000 by the end of 4 years, how much should the annual payment be
To calculate the annual payment needed to accumulate $8,000 by the end of 4 years using the Future Value of an Annuity (FVA) formula, you need to use the formula:
FVA = P * ((1+r)^n - 1) / r
Where:
FVA = Future Value of the annuity
P = Annual payment
r = interest rate per period
n = number of periods
In this case, we are given that the IF (interest factor) for the annuity is 4.5 at a 10% interest rate for 4 years. The interest factor represents the value obtained when you divide the future value by the annual payment.
So, IF = FVA / P
To calculate the annual payment (P), we rearrange the formula:
P = FVA / IF
Plugging in the values we know:
FVA = $8,000
IF = 4.5
P = $8,000 / 4.5
P ≈ $1,777.78
Therefore, the annual payment should be approximately $1,777.78