Answer: $12
Step-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 % =0.016
t= 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 .
