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.
















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(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.

Respuesta :

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