Question

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?

Answer 1

Answer: $12

Step-by-step explanation:

The formula to calculate the compound interest , if the interest is compounded semi-annually :-

$A=P[(1+\dfrac{r}{2})^{2t}-1]$

, 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 = $\dfrac{1}{2}$ year  [∵ 1 year = 12 months]

Then, the interest earned by Robert in 6 months will be :-

$A=1500[(1+\dfrac{0.016}{2})^{2\cdot\frac{1}{2}}-1]$

$A=1500[(1+0.008)^{1}-1]$

$A=1500[1.008-1]$

$A=1500[0.008]=12$

Hence, Robert earned $12 as interest .