Find the future value of an ordinary annuity of $70 paid quarterly for 5 years, if the interest rate is 10%, compounded quarterly. (Round your answer to the nearest cent.)
quarterly rate = .10/4 = .025 = i
number of payments = 4(5) = 20 = n
amount = 70( 1.025^20 - 1)/.025
= ...
where did you get the 1.025 from
To find the future value of an ordinary annuity, we can use the formula:
FV = P * [(1 + r)^n - 1] / r
Where:
FV = Future value
P = Payment amount per period
r = Interest rate per period
n = Number of periods
In this case, the payment amount per period (P) is $70, the interest rate per period (r) is 10% (or 0.10), and the number of periods (n) is 5 years multiplied by 4 quarters per year, which equals 20 quarters.
Let's plug these values into the formula:
FV = 70 * [(1 + 0.10)^20 - 1] / 0.10
Now, we can calculate the future value by simplifying the equation:
FV = 70 * [(1.10)^20 - 1] / 0.10
= 70 * [6.7275 - 1] / 0.10
= 70 * 5.7275 / 0.10
= 500.925
Therefore, the future value of the annuity is $500.93 (rounded to the nearest cent).