Question

Charlotte invests £5000.

The bank pays 10% interest for the first year and then y% every year after that.
After three years, Charlotte has £5610.55
Calculate y

Answer 1

y = 1%

Explanation:

From the formula;

Interest; i = PRT/100

P = £5000

R = 10%

After 1 year, we have;

i = 5000 × 10 × 1/100 = £500

Amount is now; 5000 + 500 = £5500

Since interest rate is now y% every year after the first one, then;

After 2nd year;

i = (5500 × y × 1)/100

i = 55y

So amount is now;

5500 + 55y

After 3rd year, interest is now;

i = (5500 + 55y) × y × 1/100

i = 55 + 0.55y²

Amount is now;

(5500 + 55y) + (55 + 0.55y²)

Since she has £5610.55 after 3 years, then;

(5500 + 55y) + (55 + 0.55y²) = 5610.55

0.55y² + 55y + 5555 - 5610.55 = 0

0.55y² + 55y - 55.55 = 0

From quadratic formula, y = 1%