what is the future value of a 5 yr. ordinary annuity due that promises to pay $300.00 each year? The rate of interest being 7%
To calculate the future value of an ordinary annuity due, which means payments are made at the beginning of each period, you need to use the future value of an ordinary annuity due formula:
FV = P * [(1 + r)^n - 1] / r
where:
FV = Future value of the annuity
P = Payment amount per period
r = Interest rate per period
n = Number of periods
In this case:
P = $300.00 per year
r = 7% per year (or 0.07 in decimal form)
n = 5 years
Plugging these values into the formula, we get:
FV = $300.00 * [(1 + 0.07)^5 - 1] / 0.07
To simplify, let's calculate (1 + 0.07)^5 first:
(1 + 0.07)^5 = 1.07^5 = 1.40255
Substituting this back into the formula:
FV = $300.00 * (1.40255 - 1) / 0.07
Now, subtract 1 from 1.40255:
1.40255 - 1 = 0.40255
And substitute this back into the formula:
FV = $300.00 * 0.40255 / 0.07
To simplify further, divide 0.40255 by 0.07:
0.40255 / 0.07 = 5.75071
Finally, multiply $300.00 by 5.75071 to get the future value:
FV = $300.00 * 5.75071
The future value of the 5-year ordinary annuity due is approximately $1,725.21.