Question

Carson invested $1,700 in an account paying an interest rate of 3(3)/(4)% compounded monthly. Peyton invested $1,700 in an account paying an interest rate of 3(5)/(8)% compounded daily. After 7 years, how much more money would Carson have in his account than Peyton, to the nearest dollar?

Answer 1

Carson would have $2,175.60 - $2,229.55 = -$53.95 less money in his account than Peyton after 7 years (to the nearest cent).

Step-by-step explanation:

To find out how much more money Carson would have in his account than Peyton after 7 years, we can use the formula for compound interest: A = P(1 + r/n)^(nt).

For Carson, P = $1,700, r = 3(3)/(4)% = 0.0375, n = 12 (monthly compounding), and t = 7.

Plugging these values into the formula gives us A = 1700(1 + 0.0375/12)^(12*7) = $2,175.60 (to the nearest cent).

For Peyton, P = $1,700, r = 3(5)/(8)% = 0.0375, n = 365 (daily compounding), and t = 7.

Plugging these values into the formula gives us A = 1700(1 + 0.0375/365)^(365*7) = $2,229.55 (to the nearest cent).

Therefore, Carson would have $2,175.60 - $2,229.55 = -$53.95 less money in his account than Peyton after 7 years (to the nearest cent).

Answer 2

Carson would have $4.89 more money in his account than Peyton after 7 years.

Step-by-step explanation:

To find out how much more money Carson would have in his account than Peyton after 7 years, we need to calculate the final amounts each person would have in their accounts and subtract the amount in Peyton's account from Carson's account.

For Carson, we use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount, r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years. Plugging in the values, we have A = 1700(1 + 3.75/100)^(12*7) = $2161.14 (rounded to the nearest cent).

For Peyton, we use the same formula but with different values: A = 1700(1 + 3.625/100)^(365*7) = $2156.25 (rounded to the nearest cent).

Therefore, Carson would have $2161.14 - $2156.25 = $4.89 (rounded to the nearest dollar) more in his account than Peyton after 7 years.