One Year Future Value: What is the future value of $6,000 deposited for one year earning 9% interest rate annually?
a) $6,540
b) $6,540.00
c) $6,540.90
d) $6,540.10
The Correct Answer and Explanation is :
The correct answer is b) $6,540.00.
Explanation:
To calculate the future value (FV) of a deposit earning interest, we use the Future Value Formula for compound interest, which is:
[
FV = P \times (1 + r)^t
]
Where:
- FV is the future value of the deposit,
- P is the principal amount (initial deposit),
- r is the annual interest rate (as a decimal),
- t is the time in years.
In this case:
- P = $6,000,
- r = 9% = 0.09,
- t = 1 year.
Now, let’s plug these values into the formula:
[
FV = 6000 \times (1 + 0.09)^1
]
[
FV = 6000 \times 1.09
]
[
FV = 6,540
]
So, the future value of the $6,000 deposited for one year at a 9% interest rate is $6,540.00.
Understanding the Calculation:
The formula reflects compound interest, meaning the interest is added to the initial deposit (principal) after each period, and the next period’s interest is calculated on the new, higher principal. In this case, since the deposit is only for one year, there is no compounding period, but the interest still accrues for the full year.
The formula assumes that the interest is compounded annually, which means the deposit earns interest once a year at the stated rate. If the interest rate were compounded more frequently (quarterly, monthly, etc.), the future value would be slightly higher due to the more frequent compounding.
The correct option is b) $6,540.00, as this is the exact amount when the interest is calculated once at the end of the year.