Question

When Alice started working, she has decided to deposit $250 a pay check into a savings account that earns an interest of 1% per month. She gets paid on the last day of every month. Which of the following expression may be used to determine the account value 10 years from now?
a. F= [250/0.01] (F/P, 1%, 60)
b. F = 250[(P/A, 1%, 120) (F/P, 12%, 5)]
c. F= 250(F/A, 1%, 120)
d. F = [3,000(P/A, 12%, 10)] [(F/P, 12%, 10)]

Answer 1

Answer:

The correct option is c. F= 250(F/A, 1%, 120).

Explanation:

Since she gets paid on the last day of every month, implies we are to the determine the future value (F) of an ordinary annuity. Therefore, the original expression for the future value (F) of an ordinary annuity is as follows:

F= A(F/A, i, n) …………………. (1)

Where:

F = Future value

A = Periodic or monthly amount = $250

F/A = Convert A to F

i = monthly interest rate = 1%

n = number of months = Number of years * number of months in a year = 10 * 12 = 120

Substituting the values into equation (1) except F/A, we have:

F= 250(F/A, 1%, 120) …………………… (1)

Therefore, the correct option is c. F= 250(F/A, 1%, 120).

Note:

Note that inputting equation into a scientific calculator will give the following future value (F):

F = $57,509.67