Respuesta :
Answer:
$2,282.78
Explanation:
This is calculated as follows:
Step 1 = Calculation of Annual ATM fees
Annual ATM fees = Service fee × Number of times the ATM is used in a year
Annual ATM fees = $2 × 200 = $200
Step 1 = Calculation of Future Value (FV) of Annual ATM fees
FV = PV × {[(1 + r)^n - 1] ÷ r} .................................. (1)
Where;
PV = Present value of Annual ATM fees = $200
r = interest rate = 3% = 0.03
n = number of years = 10
Substituting the values into equation (1), we have:
FV = $200 × {[(1 + 0.03)^10 - 1] ÷ 0.03}
= $200 × {[(1.03)^10 - 1] ÷ 0.03}
= $200 × {[1.34391637934412 - 1] ÷ 0.03}
= $200 × {0.34391637934412 ÷ 0.03}
= $200 × 11.4638793114707
= $2,292.77586229415
FV = $2,282.78 approximately
Therefore, the future value in 10 years of the annual amount paid in ATM fees is $2,282.78.
The future value in 10 years with 3% interest rate of annual amount paid in ATM fees is $2,282.78.
What is future value?
Future value (FV) is the value of a present asset at any point in the future, founded on an assumptive growth rate.
The formula of Future value is :
[tex]\text{FV}= \text{PV}\times[\dfrac{(1+i)^n-1}{i}][/tex] .................................. (1)
Where, PV is Present Value.
Computation of future value:
According to the given information,
The annual ATM fees would be:
[tex]\text{Annual ATM Fees} =\text{ Service Fee}\ \times\ \text{Number of Times the ATM is Used in a Year}\\\\\text{Annual ATM Fees} =\$2\times100\\\\\text{Annual ATM Fees} =\$200[/tex]
Present value of Annual ATM fees(PV) = $200
Interest Rate(i) = 3% = 0.03
Number of Years (n) = 10
Substituting the values into equation (1), we have:
[tex]\text{FV}= \text{PV}\times[\dfrac{(1+i)^n-1}{i}]\\\\\\\text{FV}=\$200\times[\dfrac{(1+0.03)^1^0-1}{0.03}]\\\\\\\text{FV}=\$200\times11.46\\\\FV = \$2,282.78 \text{appro}.[/tex]
Therefore, the future value in 10 years of the yearly amount paid in ATM fees would be $2,282.78.
Learn more about the future value, refer to:
https://brainly.com/question/1759639
