Answer:
The future value = $1780
Step-by-step explanation:
* Lets explain the formula of the future value
- Future Value of an annuity is used to determine the future value of a
stream of equal payments.
- The future value of an annuity formula can also be used to determine
the number of payments, the interest rate, and the amount of the
recurring payments
- The future value formula is [tex]FV=\frac{PMT}{i}(1-\frac{1}{(1+i)^{n}})[/tex]
where:
# FV = Future Value of the annuity
# PMT= Payment amount
# i = Annual interest rate
# n = Number of payments
* Lets solve the problem
- n = 27
- i = 0.04
- PMT = $109
- To find FV lets use the formula above
∵ n = 27 , i = 0.04 , PMT = 109
∴ [tex]FV=\frac{109}{0.04}(1-\frac{1}{(1+0.04)^{27}})[/tex]
∴ [tex]FV=2725(1-\frac{1}{(1.04)^{27}})=1779.9248[/tex]
∴ FV = 1779.92 ≅ 1780
∴ The future value = $1780
