Angela decided to save $100 from each paycheck to put toward a car. Twenty-six paychecks, one every other week, are deposited into a money market account with an annual interest rate of 7.5 percent. Determine the future value of the account after 4 years. Submit your answer in exact change.
Use this formula
FV = P (1+r)^n -1 / r
Using the given information:
P = $100 (amount saved from each paycheck)
r = 7.5% annual interest rate, which is 0.075 in decimal form
n = 26 paychecks per year for 4 years, so n = 26 x 4 = 104
Now, substitute these values into the formula:
FV = $100 [(1 + 0.075)^104 - 1] / 0.075
Calculating inside the brackets first:
(1 + 0.075)^104 = (1.075)^104 ≈ 8.362739
Now, plug this back into the formula:
FV = $100 [8.362739 - 1] / 0.075
FV = $100 * 7.362739 / 0.075
FV = $736.2739 / 0.075
FV = $9816.9853
Therefore, the future value of the account after 4 years is $9816.99.