1. **State the problem:**
We have £1400 deposited in an account with a simple interest rate of 7% per year.
2. **Formula for simple interest:**
The interest earned each year is given by the formula:
$$I = P \times r \times t$$
where $P$ is the principal amount, $r$ is the annual interest rate (as a decimal), and $t$ is the time in years.
3. **Calculate the interest added each year (part a):**
Given $P = 1400$, $r = 0.07$, and $t = 1$ year,
$$I = 1400 \times 0.07 \times 1 = 98$$
So, £98 is added to the account each year.
4. **Calculate the total amount after two years (part b):**
The total amount $A$ after $t$ years with simple interest is:
$$A = P + I = P + P \times r \times t = P(1 + r \times t)$$
For $t = 2$ years:
$$A = 1400 (1 + 0.07 \times 2) = 1400 (1 + 0.14) = 1400 \times 1.14 = 1596$$
**Final answers:**
- a) £98 is added each year.
- b) After two years, the account will have £1596.
Simple Interest Bc75A4
Step-by-step solutions with LaTeX - clean, fast, and student-friendly.