From the image, we have the following information:

• The Robinsons invest $2,900 in an account with an annual interest rate of 1.11%, compounded annually.
• They want to know the total amount after 2 years, assuming no withdrawals are made.

Questions:

1. (a) How much money will be in the account after 2 years?
2. (b) How much interest is earned on the investment after 2 years?

Solution using Compound Interest Formula:

The compound interest formula is: $A = P \left(1 + \frac{r}{n}\right)^{nt}$ Where:

• $A$ is the amount of money accumulated after n years, including interest.
• $P = 2900$ (the principal amount).
• $r = 0.0111$ (annual interest rate as a decimal).
• $t = 2$ years.
• $n = 1$ (since interest is compounded annually).

Part (a): Total Amount After 2 Years

$A = 2900 \left(1 + \frac{0.0111}{1}\right)^{1 \times 2}$ This gives us the total amount after 2 years.

Part (b): Interest Earned

Interest earned = Total amount $A$ - Principal $P$.

The image shows the answers as:

• (a) $2,964.74 (Total Amount)
• (b) $64.74 (Interest Earned)

Would you like me to calculate these in detail and verify them? Also, let me know if you have further questions.

Here are 5 follow-up questions based on the compound interest formula:

1. What happens if the interest were compounded quarterly instead of annually?
2. How much would the Robinsons earn after 5 years instead of 2?
3. What would the final amount be if the interest rate was 2% instead of 1.11%?
4. How would the outcome change if withdrawals were made halfway through the 2-year period?
5. What would be the effect of continuous compounding on the final amount?

Tip: Always ensure to convert the percentage interest rate into a decimal before using it in calculations (e.g., 1.11% becomes 0.0111).