Question: User: Megan invests £2000 into a savings account which gathers compound interest of 2.5% per year.
a) How much money will Megan have in the account after 7 years?
b) How much interest will Megan have earned from this account after 7 years?
Give your answers in pounds to the nearest 1p.
1. **State the problem:**
Megan invests $2000$ pounds at an annual compound interest rate of $2.5\%$ for $7$ years.
2. **Formula for compound interest:**
The amount $A$ after $t$ years with principal $P$ and annual interest rate $r$ compounded yearly is given by:
$$A = P \times (1 + r)^t$$
where $r$ is in decimal form.
3. **Convert interest rate to decimal:**
$$r = \frac{2.5}{100} = 0.025$$
4. **Calculate the amount after 7 years:**
$$A = 2000 \times (1 + 0.025)^7 = 2000 \times (1.025)^7$$
Calculate $(1.025)^7$:
$$ (1.025)^7 = 1.025 \times 1.025 \times 1.025 \times 1.025 \times 1.025 \times 1.025 \times 1.025 \approx 1.1907$$
So,
$$A \approx 2000 \times 1.1907 = 2381.4$$
5. **Round to nearest 1p:**
$$A = 2381.40$$ pounds
6. **Calculate the interest earned:**
Interest $I$ is the total amount minus the principal:
$$I = A - P = 2381.40 - 2000 = 381.40$$ pounds
**Final answers:**
- a) Megan will have approximately **2381.40** pounds after 7 years.
- b) Megan will have earned approximately **381.40** pounds in interest after 7 years.