Final answer:
The investment with a 5% interest rate compounded quarterly will earn more interest in 6 years compared to the investment with a 4.75% interest rate compounded continuously. The better plan will earn $373.88 more.
Step-by-step explanation:
To determine which investment will earn more interest in 6 years, we can calculate the future value (FV) of the investments using the compound interest formula. For the first investment with a 5% interest rate compounded quarterly, the formula is:
FV = P(1 + r/n)^(nt)
where P is the initial principal ($60,000), r is the annual interest rate (5%), n is the number of compounding periods per year (4 for quarterly), and t is the number of years (6). Plugging in the values, we get:
- FV1 = $60,000(1 + 0.05/4)^(4*6) = $72,586.67
For the second investment with a 4.75% interest rate compounded continuously, the formula is:
FV = Pe^(rt)
where e is the base of natural logarithms and t is the number of years (6). Plugging in the values, we get:
- FV2 = $60,000e^(0.0475*6) = $72,212.79
Therefore, the first investment will earn more interest with a future value of $72,586.67 compared to $72,212.79 for the second investment.
To calculate how much more the better plan will earn, we subtract the future value of the second investment from the future value of the first investment:
- Difference = FV1 - FV2 = $72,586.67 - $72,212.79 = $373.88
Therefore, the better plan will earn $373.88 more.