Question

Carter invested $1,200 in an account paying an interest rate of 7 3/4% compounded continuously. scarlett invested $1,200 in an account paying an interest rate of 8 1/4% compounded monthly. to the nearest dollar, how much money would carter have in his account when scarlett's money has doubled in value?

Answer 1

To determine how much money Carter will have in his account when Scarlett's money has doubled in value, we need to find the time it takes for Scarlett's money to double. Using the compound interest formula for continuous compounding, we can calculate that Carter will have approximately $2,706 in his account.

Step-by-step explanation:

To determine how much money Carter will have in his account when Scarlett's money has doubled in value, we need to find the time it takes for Scarlett's money to double. We can use the compound interest formula for continuous compounding:

A = P*e^(rt)

Where A is the final amount, P is the principal amount, r is the interest rate, and t is the time in years. Let's calculate:

1. For Scarlett: A = 1200*2 = 2400 dollars
2. For Carter: A = 1200*e^(0.0775t)

Now we can solve for t by setting the two equations equal to each other and solving for t:

1200*e^(0.0775t) = 2400

e^(0.0775t) = 2400/1200

e^(0.0775t) = 2

0.0775t = ln(2)

t = ln(2) / 0.0775

Solving this gives us approximately t = 8.96 years. Now we can substitute this value into the equation for Carter's account:

A = 1200*e^(0.0775*8.96)

A ≈ 1200*2.2556 ≈ ~$2,706