Kay invests £1500 in an account paying 3% compound interest per year - OCR - GCSE Maths - Question 23 - 2019 - Paper 1

Neil's investment uses the formula for simple interest:

$A = P(1 + rt)$

Where:

• A = final amount
• P = principal amount (£1500)
• r = rate of interest (expressed as a decimal)
• t = time in years (5)

So:

$A = 1500(1 + 5r)$

Since after 5 years both accounts contain the same amount, we equate Neil's amount to Kay's:

$1500(1 + 5r) = 1738.91$

Now, we can solve for r:

1. Expand Neil's equation: $1500 + 7500r = 1738.91$
2. Subtract 1500 from both sides: $7500r = 1738.91 - 1500$ $7500r = 238.91$
3. Divide by 7500: $r = \frac{238.91}{7500} \\ \approx 0.031855$
4. Convert to percentage: $r \approx 3.2\%$

Thus, the value of r is approximately 3.2%.