At the beginning of each year for 14 years, Sherry Kardell invested $400 that earns 10% annually. What is the future value of Sherry's account in 14 years?
A. $14,000 B. $13,100 C. $12,309 D. $12,709
Answer: D?
I've calculated several times and come out with C or D please help!
To calculate the future value of an investment, you can use the formula:
Future Value = Present Value * (1 + Interest Rate)^Number of Years
In this case, Sherry invested $400 at the beginning of each year for 14 years, and the interest rate is 10%.
Let's calculate the future value step by step:
1. Calculate the future value of each individual investment:
First Year: $400 * (1 + 0.10) = $440
Second Year: $400 * (1 + 0.10)^2 = $484
Third Year: $400 * (1 + 0.10)^3 = $532.40
...
14th Year: $400 * (1 + 0.10)^14 = $1509.49
2. Calculate the total future value by summing up all the individual investments:
Total Future Value = $440 + $484 + $532.40 + ... + $1509.49
To calculate the sum of this series of investments, you can use the formula for the sum of a geometric series:
Sum = (First Term * (1 - Common Ratio^Number of Terms)) / (1 - Common Ratio)
In this case, the first term is $440, the common ratio is (1 + 0.10), the number of terms is 14.
Let's calculate the total future value:
Sum = ($440 * (1 - (1 + 0.10)^14)) / (1 - (1 + 0.10))
Sum = ($440 * (1 - 1.10^14)) / (1 - 1.10)
Sum = ($440 * (1 - 1.593848)) / (-0.10)
Sum = ($440 * -0.593848) / (-0.10)
Sum = $260.99
Therefore, the future value of Sherry's account in 14 years is $260.99.
Based on the answer choices given, none of them are correct.
To calculate the future value of Sherry's account, you can use the formula for compound interest:
FV = PV * (1 + r)^n
Where:
FV = Future value of the account
PV = Present value or initial investment (in this case $400)
r = Interest rate per period (in this case 10% or 0.10)
n = Number of periods (in this case 14 years)
Substituting the values given, we get:
FV = $400 * (1 + 0.10)^14
Now let's calculate the answer:
FV = $400 * (1.10)^14
FV = $400 * 1.9487171...
Rounding the result to the nearest dollar, we get:
FV ≈ $779.49
Therefore, the correct answer is not among the options you provided. The closest option is C. However, the most accurate answer would be $779 since the question asks for the future value rounded to the nearest dollar.
400*1.1^14 + ... + 400*1.1^1
= 400(1.1^15-1)/(1.1-1)
= 12709