1

Problem

Two investments were made, as shown in the table. The interest in Account A is compounded once per year. Which of the following is true about the investments?

2

Step

Identify the Interest type for Account A:

Compounded Interest (interest earned on both principal and accumulated interest)

3

Step

Identify the Interest type for Account B:

Simple Interest (interest earned only on the principal amount)

4

Step

Formula for Interest:

We don’t need the exact formulas here, but understanding the concept is key:

→ Compounded Interest: Involves an exponential term where interest is
calculated on a growing base (principal + previous interest). → Simple Interest: Interest is a flat rate multiplied by the principal amount.

5

Step

Impact on Future Earnings for Account A:

Due to compounding, the interest earned each year will be slightly higher than the previous year. This is because the base amount (on which interest is calculated) increases with each year’s accumulated interest.

6

Step

Impact on Future Earnings for Account B:

The interest earned remains constant at $25 every year because it’s calculated only on the initial principle, not the growing balance.

7

Step

Long-term Growth:

→ Even though Account B starts with a higher investment, Account A’s Compounding interest will cause its total interest to grow faster over time
→ This means Account A will eventually earn more interest per year than Account B.

8

Step

Example with Calculations (Assuming a one-year investment period):

Account A: → Principal (P) = $500 → Interest Rate ® = 6% →\$"Interest" (I) = P \times R = $500 \times 6% = $30 (Year 1)\$ → Year 2: Interest will be calculated on the new principal, which is the original amount + Year 1’s interest (P + I from Year 1). This means the interest earned in Year 2 will be slightly higher than $30.

Account B: → Interest = $25 (Year 1 and every subsequent year).

9

Solution

Therefore, neither the statement that Account A always earns less money per year than Account B nor the statement that Account A earns less money than Account B at first can be true.

10

Sumup

Please summarize steps

Choices

11

Choice-A

This is true because Account A benefits from compounding interest. Each year, the interest is calculated not just on the initial investment but also on the accumulated interest from previous years. This snowball effect makes Account A’s earnings grow faster than Account B’s flat, simple interest

Correct Account A always earns more money per year than Account B.

12

Choice-B

This is incorrect. Even though Account B starts with a higher investment, compounding interest in Account A will eventually lead to higher annual earnings

Wrong Account A always earns less money per year than Account B.

13

Choice-C

This is not true. Due to compounding, Account A’s earnings will continue to grow each year, not decrease

Wrong Account A earns more money per year than Account B at first but eventually earns less money per year.

14

Choice-D

This could be tempting, but remember that compounding starts working immediately. Even in the first year, Account A’s interest will likely be slightly higher than Account B’s due to the small amount of interest earned on the initial investment. The gap in earnings will widen over time

Wrong Account A earns less money per year than Account B at first but eventually earns more money per year.

15

Answer

Option

A

16

Sumup

Please summarize choices