Robert Duncan made a $1500 deposit to savings account paying 1.6 annual interest compounded semi annually if he kept the money on the deposit for six months how much interest did Robert earn?
Question
Answer:
Answer: $12Step-by-step explanation:The formula to calculate the compound interest , if the interest is compounded semi-annually :-[tex]A=P[(1+\dfrac{r}{2})^{2t}-1][/tex] , where P = Principal amount r = rate of interest ( in decimal)t= Time ( in years)Given : P= $1500 r= 1.6 % =0.016t= 6 months = [tex]\dfrac{1}{2}[/tex] year [∵ 1 year = 12 months]Then, the interest earned by Robert in 6 months will be :-[tex]A=1500[(1+\dfrac{0.016}{2})^{2\cdot\frac{1}{2}}-1][/tex] [tex]A=1500[(1+0.008)^{1}-1][/tex] [tex]A=1500[1.008-1][/tex] [tex]A=1500[0.008]=12[/tex] Hence, Robert earned $12 as interest .
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