Question

(30 POINTS) A newly hired lawyer receives a $15,000 signing bonus from a law firm and invests the money in a savings account at 4.75% interest. After 42 months, the lawyer checks the account balance.

Part A: Calculate the interest earned, to the nearest dollar, if the interest is compounded quarterly. Show all work. (2 points)

Part B: Calculate the interest earned, to the nearest dollar, if the interest is compounded continuously. Show all work. (2 points)

Part C: Using the values from Part A and Part B, compare the interest earned for each account by finding the difference in the amount of interest earned. (1 point)

Answer 1

Part A: The interest earned with quarterly compounding is approximately $3,195. Part B: The interest earned with continuous compounding is approximately $3,253. Part C: The difference in the amount of interest earned between the two accounts is $58.

Step-by-step explanation:

Part A: To calculate the interest earned, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

• A is the final amount
• P is the principal amount (initial investment)
• r is the annual interest rate (as a decimal)
• n is the number of times interest is compounded per year
• t is the number of years

Using the given information, we can plug in the values:

A = 15,000(1 + 0.0475/4)^(4*42)

Calculating this, we find that the interest earned is approximately $3,195.

Part B: To calculate the interest earned with continuous compounding, we can use the formula:

A = Pe^(rt)

Plugging in the values, we get:

A = 15,000e^(0.0475*42)

Calculating this, we find that the interest earned is approximately $3,253.

Part C: To find the difference in the amount of interest earned between the two accounts, we subtract the interest earned with quarterly compounding from the interest earned with continuous compounding:

Difference = $3,253 - $3,195 = $58.