Question

Fatima opened a savings account with $7,500. She decided to deposit that same amount semiannually. This account earns 3.975% interest compounded semiannually. What is the future value of the account after 10 years?

Options:
A) $7,500
B) $8,214.54
C) $9,000
D) $10,000

Answer 1

The future value of the account after 10 years is approximately $9,000.

Step-by-step explanation:

To find the future value of the account after 10 years, we can use the formula for compound interest:

FV = P(1+r/n)^(nt)

Where:

• FV = future value
• P = initial principal (amount deposited)
• r = annual interest rate (in decimal form)
• n = number of times interest is compounded per year
• t = number of years

In this case, Fatima deposits $7,500 semiannually, so the principal (P) is $7,500. The annual interest rate (r) is 3.975% (expressed as 0.03975), and the interest is compounded semiannually, so n = 2. Fatima wants to find the future value after 10 years, so t = 10. Plugging in these values, we have:

FV = 7500(1+0.03975/2)^(2*10)

Calculating this, the future value of the account after 10 years is approximately $9,000. Therefore, the correct option is C) $9,000.