Question

Mr. Smith invests a sum of money at a 4% per annum interest rate, compounded annually. He also invests the same amount of money at the same interest rate for a period of 2 years and 3 months. Calculate the difference between the simple interest and compound interest earned in this duration.

Options:

A) $112.48
B) $115.20
C) $118.36
D) $121.05
E) $124.40

Answer 1

To find the difference between simple interest and compound interest for Mr. Smith's investment over 2 years and 3 months at a 4% interest rate, compound interest formula A = P * (1 + r/n)^(nt) and simple interest formula I = P * r * t are used. The specific solution would involve calculating each type of interest and finding the difference, though the problem's answer is not directly computed here.

Step-by-step explanation:

We have a situation where Mr. Smith has made two investments at a 4% per annum interest rate, one compounded annually and the other offering simple interest, for a period of 2 years and 3 months. We need to calculate the difference between the simple interest and compound interest earned over this duration.

Using the provided information (not the exact task information but rather the educational concept), a principal amount of $100 at a 4% annual interest is considered.

For simple interest, we would calculate the interest using the formula:
I = P * r * t, where I is the interest, P is the principal, r is the rate, and t is the time in years.

In the case of compound interest, the total amount after 2 years and 3 months would be calculated using the formula:
A = P * (1 + r/n)^(n*t), where A is the future value, P is the principal, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the time in years. In this particular problem, we need to adjust our equation for the 3 month period by converting it to a decimal (0.25 years).

Worksteps for Compound Interest Calculation:

1. Calculate the amount after 2 years using the compound interest formula.
2. Adjust the amount for the additional 3 months period at the 4% interest rate.
3. Calculate the simple interest for the 2 years and 3 months period.
4. Find the difference between the two interest amounts calculated.

Although the answer options and the correct choice were not calculated, the explanation above outlines the method one would use to find the difference between simple and compound interest over the given time period. Note that as per the instructions and hints given, compound interest earns slightly more than simple interest, owing to the interest on the accumulated interest.