Donald plans to invest x dollars in a savings account that pays interest at an annual rate of 8% compounded quarterly. Approximately what amount is the minimum that Donald will need to invest to earn over $100 in interest within 6 months? Select:
A) 1500
B) 1750
C) 2000
D) 2500
E) 3000
Compound interest formula   A = P ( 1+r/n)power nt   given, n= 4 (quaterly);r =.08   the approach is substitution,   our interest requirement is 100$ after 6 months, 2 compounding period. interest per compounding period is 2%   lets take 1500, after 3 months interest accumulated is 30$, total amount is 1530   after 6 months, interest is 30.6$ and total is 1560.6$, so not 1500   1500 &amp; 1750 have a difference of 250$ only , but the expected interest different is around 40$ hence you can straightaway rule out 1750   2000 is again can be ruled out as approx 4% interest yeilds only 80$   2500$ is a good bet, first 3 months it earns 50$ as interest, next 3 months it will earn 51$ as interest.   hence answer is 2500
<result>D</result>
Donald plans to invest x dollars in a savings account that pays interest at an annual rate of 8% compounded quarterly. Approximately what amount is the minimum that Donald will need to invest to earn over $100 in interest within 6 months?