Alecia deposited $500 in a savings account at 5% compounded semiannually. What is her balance after 5 years?
Can you please show me step by step how to do this problem.
The choices are
$650.00
$640.04
$670.05
$897.93
you have 10 periods.
total=500(1+.05/2)^10=500(1.025)^10
Put this in your google Seearch window:
500(1.025)^10=
To find Alecia's balance after 5 years, we need to use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount or balance
P = the principal amount (initial deposit)
r = the annual interest rate (in decimal form)
n = the number of times interest is compounded per year
t = the number of years
In this case, Alecia deposited $500, the interest rate is 5%, compounded semiannually. So we have:
P = $500
r = 0.05 (since 5% is 0.05 in decimal form)
n = 2 (semiannual compounding means twice a year)
t = 5 (5 years)
Now, we can plug these values into the formula:
A = $500(1 + 0.05/2)^(2*5)
First, divide the interest rate by the number of compounding periods per year: 0.05/2 = 0.025.
Then, add 1 to this value: 1 + 0.025 = 1.025.
Next, raise this result to the power of the number of total compounding periods over the given time: (1.025)^(2*5).
Calculating the exponential part: (1.025)^10 = 1.280084.
Finally, multiply this result by the principal amount: A = $500 * 1.280084 = $640.042.
Therefore, Alecia's balance after 5 years is approximately $640.04.
So, the correct answer is $640.04.