Kay invests £1500 in an account paying 3% compound interest per year - OCR - GCSE Maths - Question 5 - 2019 - Paper 1

To find the amount in Neil's account after 5 years with r% simple interest, we use the formula for simple interest:

$A = P(1 + rt)$

Where:

• A is the total amount after time t.
• P is the principal amount.
• r is the annual interest rate (as a decimal).
• t is the time in years.

For Neil:

• P = £1500
• r = \frac{r}{100}
• t = 5

Calculating:

Since Kay's and Neil's accounts contain the same amount of money at the end of 5 years, we set the amounts equal to each other:

$1738.91 = 1500 + 75r$

Now, solving for r:

1. Subtract 1500 from both sides: $1738.91 - 1500 = 75r$ $238.91 = 75r$

2. Divide both sides by 75: $r = \frac{238.91}{75} \approx 3.18546667$

3. Rounding to 1 decimal place gives: $r \approx 3.2$