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Let's address the questions visible in the image step by step:

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### **Question 1:**
**Tom invests €1283 at 7.4% per year. How much is the investment worth after 5 years?**

This is a compound interest problem. The formula for compound interest is:

\[
A = P(1 + r)^t
\]

Where:
- \(A\) is the amount of money after \(t\) years,
- \(P\) is the principal (initial investment),
- \(r\) is the annual interest rate (in decimal),
- \(t\) is the number of years.

Here:
- \(P = 1283\),
- \(r = 7.4\% = 0.074\),
- \(t = 5\) years.

Now we can calculate:

\[
A = 1283(1 + 0.074)^5
\]

First, calculate \(1 + 0.074 = 1.074\), then raise to the power of 5:

\[
A = 1283 \times (1.074)^5 \approx 1283 \times 1.42919 = 1833.94
\]

Thus, Tom's investment will be worth **€1833.94** after 5 years.

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### **Question 2:**
**How much must Mary invest today in order to have €4461 in 9 years if the interest rate is 8.3% per annum?**

This is a present value problem, where we rearrange the compound interest formula to solve for \(P\):

\[
P = \frac{A}{(1 + r)^t}
\]

Where:
- \(A = 4461\),
- \(r = 8.3\% = 0.083\),
- \(t = 9\) years.

Now let's calculate:

\[
P = \frac{4461}{(1 + 0.083)^9}
\]

First, calculate \(1 + 0.083 = 1.083\), then raise to the power of 9:

\[
P = \frac{446

Tom invests €1283 at 7.4% per year. How much is the investment worth after 5 years? How much must Mary invest today in order to have €4461 in 9 years if the interest rate is 8.3% per annum? What annual interest rate, to two places of decimal, will turn €1517 into €1881 after 6 years?

Solve compound interest problems for investments and calculate the present value needed for future goals. This example includes calculating the future value of €1283 at 7.4% interest after 5 years, determining the investment required to grow to €4461 in 9 years at 8.3%, and finding the interest rate needed to turn €1517 into €1881 over 6 years.

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