Question

Hannah and Dawson have both invested money in savings accounts with APYs of 3.2%. If Hannah's account has a balance of $31,000 and Dawson's account has a balance of $42,000, how much more interest does Dawson earn than Hannah?

Answer 1

To calculate the difference in interest earned by Hannah and Dawson, we need to calculate the interest earned by each of them using the compound interest formula. Hannah's account with a balance of $31,000 and an APR of 3.2% will have a final amount of $31,992.80. Dawson's account with a balance of $42,000 and an APR of 3.2% will have a final amount of $43,344. Therefore, Dawson earns $1,344 more interest than Hannah.

Step-by-step explanation:

To calculate the difference in interest earned by Hannah and Dawson, we need to calculate the interest earned by each of them first.

The formula to calculate interest is A = P(1+r/n)^(nt), where A is the final amount, P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.

For Hannah, the principal amount is $31,000 and the annual interest rate is 3.2%. Let's assume the interest is compounded annually. So, the calculation is A = 31,000(1+0.032/1)^(1*1), which gives us a final amount of $31,992.80.

For Dawson, the principal amount is $42,000 and the annual interest rate is also 3.2%. Using the same assumption of annual compounding, the calculation is A = 42,000(1+0.032/1)^(1*1), which gives us a final amount of $43,344.

Now, we can calculate the difference in interest earned by subtracting the initial balance from the final amounts. Dawson earns $43,344 - $42,000 = $1,344 more interest than Hannah.