Answer:
a. $10,100.25
b. $10,100.00
Explanation:
a. When annual interest rate i is compounded n times per year, the multiplier for each compounding period is 1+i/n. Here, we have i=.02 and n=4, so the multiplier on the account balance each quarter is 1+.02/4 = 1.005.
In two quarters (6 months) the original account balance of $10,000 is multiplied by 1.005 two times:
6-month balance = $10,000×1.005² = $10,100.25
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b. For simple interest the formula for the account balance is ...
A = P(1 +rt) . . . . . P is the principal, r is the annual rate, t is the number of years
For this problem, we have P=10,000, r=.02, t=0.5, so the account balance after 6 months of simple interest is ...
A = $10,000(1 +.02·0.5) = $10,000×1.01 = $10,100.00