Final answer:
The compound amount for a deposit of $2,000 at 7% compounded quarterly for 3 years, after rounding to the nearest cent, is $2,459.69. Therefore, the correct answer is B) $2,462.88.
Step-by-step explanation:
To find the compound amount for a deposit of $2,000 at 7% compounded quarterly for 3 years, we use the formula for compound interest:
A = P(1 + r/n)(nt)
Where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial amount of money).
- r is the annual interest rate (decimal).
- n is the number of times that interest is compounded per year.
- t is the time the money is invested for, in years.
Given:
- P = $2,000
- r = 7/100 = 0.07 (as a decimal)
- n = 4 (since interest is compounded quarterly)
- t = 3 years
Now, substituting the values into the formula:
A = 2000 (1 + 0.07/4)(4 * 3)
A = 2000 (1 + 0.0175)12
A = 2000 (1.0175)12
A = 2000 * 1.229847
A = $2,459.69
Therefore, after rounding to the nearest cent, the compound amount is $2,459.69.
Answer: B) $2,462.88