Question

Mrs. Stevens wants to have $18,000 in the bank in 3 years. If she deposits $9500 today at 4% compounded quarterly for 3 years, how much additional money will she need to add after three years to her investment to make her balance $18000?

a.
$8356.79
b.
$0
c.
$7295.16
d.
$10,704.84

Answer 1

To find out how much additional money Mrs. Stevens will need to add after three years to her investment to make her balance $18,000, we need to calculate the future value of her initial deposit and subtract it from $18,000.

Step-by-step explanation:

To find out how much additional money Mrs. Stevens will need to add after three years to her investment to make her balance $18,000, we need to calculate the future value of her initial deposit and then subtract it from $18,000.

Step 1: Convert the annual interest rate to a quarterly rate: 4% / 4 = 1%

Step 2: Convert the number of years to the number of quarters: 3 years * 4 = 12 quarters

Step 3: Calculate the future value of the initial deposit: Future value = $9500 * (1 + 0.01)^12 = $10,704.84

Step 4: Calculate the additional money needed: Additional money = $18,000 - $10,704.84 = $7295.16

Therefore, Mrs. Stevens will need to add $7295.16 after three years to her investment to make her balance $18,000.

Answer 2

A=p(1+i/m)^mn
A=9,500×(1+0.04÷4)^(4×3)
A=10,704.84
The balance she needs

18,000−10,704.84
=7,295.16