maths past paper question

alfamale

hi can somebody please explain the solution to this question from 2008 paper 1 c. In particular where has the 2.04 come from?

Walter wishes to pay off his loan in equal instalments at the end of the first
and second year. The rate remains at 4% per annum compound interest.
􀀢 How much would he need to repay, at the end of each year, to clear his
loan after two years? Give your answer correct to the nearest cent.

Solution:

Let the equal instalment be x
P Year 1 = €5000
P Year 2 = €5000 × 1·04 - x = €5200 -x
P Year 3 = (€5200 -x) × 1·04 = x Final payment
(€5200 - x) x 1·04 = x
€5408 - 1.04x = x
€5408 = 2.04x
x = €5408/ 2.04 = €2650.98

brownacid

x +1.04x = 2.04x

alfamale

brownacid wrote: »

x +1.04x = 2.04x

That's the bit i don't understand.

gerardo1982

As the previous poster said:

x + 1.04x = 2.04x

The x on it's own is the same as 1x.

You could also write it this way:

1x +1.04x = 2.04x

alfamale

thanks, easy when you know.

gerardo1982

It's the same with most things in life, anyway good luck with your studies.