Katie invests $5,000 in an account earning 4% interest, compounded annually for 5 years. Two years after Katie's initial investment, Emily invests $10,000 in an account earning 4% interest, compounded annually for 3 years. Given that no additional deposits are made, compare the amount of interest earned after the interest period ends for each account. (round to the nearest dollar) A) Katie earned $408 more in interest in her account than Emily. B) Emily earned $408 more in interest in her account than Katie. C) Katie earned $166 more in interest in her account than Emily. D) Emily earned $166 more in interest in her account than Katie.
Accepted Solution
A:
Emily earned $166 more in her account than Katie.
We use the compound interest formula for both of these:
[tex]A=p(1+r)^t[/tex]
For Katie's deposit: [tex]A=5000(1+0.04)^5=5000(1.04)^5 = 6083.26[/tex]
This gives Katie 6083.26-5000 = 1083.26 in interest (1083, to the nearest dollar).
For Emily's deposit: [tex]A=10000(1+0.04)^3=10000(1.04)^3=11248.64[/tex]
This means she earned 11248.64-10000=1248.64 in interest (1249, to the nearest dollar).
The difference in interest is given by 1249-1083=166