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vovikov84 [41]
2 years ago
5

Robert Duncan made a $1500 deposit to savings account paying 1.6 annual interest compounded semi annually if he kept the money o

n the deposit for six months how much interest did Robert earn?
Mathematics
1 answer:
Ahat [919]2 years ago
3 0

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 .

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We first expand the binomial squared, so we get

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