Katy invests £2000 in a savings account for 3 years.

The account pays compound interest at an annual rate of

2.5% for the first year

x% for the second year

x% for the third year

There is a total amount of £2124.46 in the savings account at the end of 3 years.

(a) Work out the rate of interest in the second year.

...

(4)

Katy goes to work by train.

The cost of her weekly train ticket increases by 12.5% to £225

(b) Work out the cost of her weekly train ticket before this increase.

1)

2000 + 0.025*2000 = £ 2050 after first year

2050+2050*x/100=2050 (1+x/100) after second year

2050 (1+x/100) + 2050 (1+x/100) * x/100 = 2050 (1+x/100) (1+x/100) = = 2050 (1+x/100) ² after third year

2050 (1+x/100) ² = 2124.46

(1+x/100) ² = 2124.46/2050

1+x/100 = √ (2124.46/2050)

x/100 = √ (2124.46/2050) - 1

x = (√ (2124.46/2050) - 1) * 100

x=1.80%

4) x - the cost of the weekly train ticket before the increase.

x+x*0.125=1.125x - the cost of the weekly ticket after increase

1.125x = 225

x=225/1.125 = £ 200