Question 1172746
the future value of an annuity with beginning of time period payments formula that i have is:


FUTURE VALUE OF AN ANNUITY WITH BEGINNING OF TIME PERIOD PAYMENTS


f = ((a*((1+r)^n-1))/r)*(1+r)


f is the future value of the annuity.
a is the annuity.
r is the interest rate per time period.
n is the number of time periods


your formula is:


FV (annuity due) = payment x (1+i)^n-1/i x (1+i)


the following inputs are being used.


payment at the beginning of each time period = 130
interest rate per time period = .06 per year / 12 = .005 per month.
number of months = 17


with my formula:


f = ((a*((1+r)^n-1))/r)*(1+r) becomes:
f = ((130*((1+.005)^17-1))/.005)*(1+.005) = 2312.152429.


with your formula:


FV (annuity due) = payment x (1+i)^n-1/i x (1+i) becomes:
FV = 130 * (1 + .005) ^ 17 - 1 / .005 * (1 + .005)
there are parentheses missing that will not get you the right answer.
i provides the parentheses required below:]
FV = 130 * ((1 + .005) ^ 17 - 1) / .005 * (1 + .005) = 2312.152429


these parentheses are very important.
one small mistake can throw the answer off big time.


i also confirmed through the use of a financial calculator.
the answer is the same.
the calculator uses the percent rate rather than the rate.
percent rate = 100 * rate.
rate = percent rate / 100
the results of using that calculator are shown below.
<img src = "http://theo.x10hosting.com/2021/011102.jpg" >