Alecia deposited $500 in a savings account at 5% compounded semiannually. What is her balance after 6 years? Please solve this question with steps.
To solve this question, we need to use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the final balance (amount after 6 years)
P = the initial deposit ($500)
r = the interest rate as a decimal (5% = 0.05)
n = the number of times the interest is compounded per year (semiannually = 2)
t = the number of years (6)
Plugging in the values into the formula:
A = 500(1 + 0.05/2)^(2*6)
Step 1: Simplify the expression within the parentheses:
A = 500(1.025)^(12)
Step 2: Raise the simplified expression to the power of 12:
A = 500(1.025)^12
Step 3: Calculate the value inside the parentheses:
A = 500(1.795856)
Step 4: Multiply the initial deposit by the value in step 3:
A = 897.928
So, after 6 years, Alecia's balance in her savings account will be approximately $897.93.
5% semiannually means 2.5% per compounding period
balance = 500 * [1 + (2.5%)]^(6 * 2)
b = 500 * (1.025)^12