Question

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)

Answer 1

Emily will earn $166 more interest than Katie after the interest period ends for each account.

Explanation:

Formula for compound interest is:
`A=P(1+(r)/(n))^n^t`, where P is the initial amount, A is the final amount with interest, r is the rate of interest in decimal, n is the number of compounding in a year and t is the time duration

Katie invests $5,000 in an account earning 4% interest, compounded annually for 5 years. That means here,
`P= 5000, r= 4\%=0.04, n=1` and
`t=5`

So,
`A= 5000(1+(0.04)/(1))^(^1^)^(^5^) = 5000(1.04)^5 = 6083.26... \approx 6083`

Thus, the amount of interest earned by Katie
`= \$6083-\$5000 = \$1083`

Now, Emily invests $10,000 in an account earning 4% interest, compounded annually for 3 years. That means here,
`P= 10000, r= 4\%=0.04, n=1` and
`t=3`

So,
`A= 10000(1+(0.04)/(1))^(^1^)^(^3^) = 10000(1.04)^3 = 11248.64 \approx 11249`

Thus, the amount of interest earned by Emily
`= \$11249-\$10000 = \$1249`

After the interest period ends for each account, Emily will earn ($1249 - $1083) or $166 more interest than Katie.