Question

John deposited $10,000 to open a new savings account that earned 4 percent annual interest, compounded quarterly. If there were no other transactions in the account, what was the amount of money in John's account 6 months after the account was opened?

• A. $10,100
• B. $10,101
• C. $10,200
• D. $10,201
• E. $10,400

Hint:

For compound interest, remember to adjust the interest rate and time according to the number of periods.

Answer 1

The Correct Option is B

Step 1: Formula for compound interest.
The formula for compound interest is: \[ A = P \left( 1 + \frac{r}{n} \right)^{nt} \] Where:
- \( A \) is the amount in the account after time \( t \),
- \( P \) is the principal (initial deposit),
- \( r \) is the annual interest rate,
- \( n \) is the number of times the interest is compounded per year,
- \( t \) is the time in years.
Step 2: Substitute known values.
In this case:
- \( P = 10,000 \),
- \( r = 0.04 \) (4 percent annual interest),
- \( n = 4 \) (quarterly compounding),
- \( t = 0.5 \) years (6 months).
Substitute into the formula: \[ A = 10,000 \left( 1 + \frac{0.04}{4} \right)^{4 \times 0.5} = 10,000 \left( 1 + 0.01 \right)^2 = 10,000 \times (1.01)^2 \] Step 3: Calculate the final amount.
\[ A = 10,000 \times 1.0201 = 10,201 \] \[ \boxed{10,201} \]