Urgent help please!!!

I am revising for my maths exam tomorrow and have come across a question I have failed to answer and I was wondering if anyone could help me
This is the question;
Katy pays £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 three years.
a) work out the rate of interest in the second year.
b) Katy goes to work by train. The cost of her weekly train ticket increases by 12.5% to £225. Work out the cost of her weekly train ticket before the increase.

Any help will be greatly appreciated!!

Reply 1

titfortat

12

I think the first step, by just reading the question is just recognising that the interest in the second and third years are the same. What exactly do you not understand in the question?

Reply 2

Naomeyz_01

OP

10

how to work it out for the second and third year

Reply 3

Naomeyz_01

OP

10

when I see the algebra percentages I get really confused

Reply 4

titfortat

12

@Naomeyz_01

Use this simplified equation that I think is easier to use:

Initial amount x compound interest ^ no. of years = total after

I'll give you a head start:

2000 x 1.025 x ...........
Its awfully difficult to explain, but I don't think that I can post solutions instantly because of the moderation rules.

Reply 5

titfortat

12

Original post by Naomeyz_01

I am revising for my maths exam tomorrow and have come across a question I have failed to answer and I was wondering if anyone could help me
This is the question;
Katy pays £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 three years.
a) work out the rate of interest in the second year.
b) Katy goes to work by train. The cost of her weekly train ticket increases by 12.5% to £225. Work out the cost of her weekly train ticket before the increase.

Any help will be greatly appreciated!!

I have an answer. If possible, post up your working out if you think you have an answer and I'lllet you know if you've got it :smile:

Reply 6

Naomeyz_01

OP

10

where did get 1.025 from?

Posted from TSR Mobile

Reply 7

hopefullyadoctor

After the first year there will be £2000 x 1.025 which is £2050

For the second and third year, the expontential increase is x%

So the second year will be 2050 times x%and the third year will be (2050 times x%) times x% which simplifies to 2050 times x^2

so we get the equation 2050 x x^2 = 2124.46

2124.46/2050 = x^2 = 1.036...

if we root that it should give us x, which = 1.017998994, which is 1.017998994 % per year (roughly 1.0178%)

To check:

2000 x 1.025 = 2050
2050 x1.0178 = 2086.49
2209.9 x 1.0178 = 2123.4 which is roughly correct (I have rounded the % increase, if you do the calculation without rounding you get the exact answer)

PART B:

£225 = 112.5%

divide both sides by 112.5:

2= 1%

times both sides by 100:

£200 = 100%

So the original price was £200

Hope this helps and good luck for your exam!!