Final answer:
Anna would receive approximately $26,918.81 after lending $20,000 at a 6% annual return compounded continuously for 5 years. This amount rounds up to $27,000, and since it's more than the $26,793.44 she would have received with weekly compounding, it shows that she made the right choice lending to the attorney firm.
Step-by-step explanation:
To calculate the total amount Anna received after lending $20,000 at an annual 6% return compounded continuously, we use the formula for continuous compounding: A = Pert, where A is the total amount, P is the principal, e is the base of the natural logarithm (approximately 2.71828), r is the annual interest rate (as a decimal), and t is the time in years.
Applying the formula, we get:
- P = $20,000
- r = 6% or 0.06
- t = 5 years
A = 20000 * e(0.06*5)
After calculating, we get A ≈ $26,918.81, which when rounded to the nearest $100 is $27,000.
If Anna had chosen the 6% interest compounded weekly option, we would use the formula for compound interest: A = P(1 + r/n)nt, where n is the number of times the interest is compounded per year. Since there are 52 weeks in a year, n would be 52.
Applying the formula for weekly compounding, we get:
A = 20000 * (1 + 0.06/52)52*5
The result of this calculation is A ≈ $26,793.44, which is less than what she'd receive with continuous compounding. Therefore, Anna made the right choice by lending to the attorney firm rather than to her friend.