Forex And Percentage Problem

The FOREX value (Number of INR for 1 USD) varies as follows during a certain period:  

In the 1^st quarter of a year, it increases by d%. In the 2^nd quarter of a year, it decreases by d%. In the 3^rd quarter of a year, it increases by d%. In the 4^th quarter of a year, it decreases by d%.

It is also noted that the FOREX value decreases by 200 points in the first 2 quarters and by 192 units in the last 2 quarters of the year.

If a person had 100 USD all throughout the year, what is the overall loss percentage of the value of USD, when exchanged with INR, from the start to the end of the year?  

Solution:

There are two variables here

Let's assume exchange rate = x. d is another variable which is a fraction. for 20%, d=0.2

The rate at the end of each quarter is 

1  x*(1+d)

2  x*(1+d)(1-d)=x*(1-d^2)

3  x*(1-d^2)*(1+d)

4  x*(1-d^2)^2

Now the value decreases by 200 points meaning by Rs2 after 1st 2 quarters.

Hence x - x*(1-d^2)=2 or x*[1-(1-d^2)]=2 or x*d^2=2 ---------------(A)

The value decreases by 192 points in the last 2 quarters

Hence, x*(1-d^2)-x*(1-d^2)^2=1.92 or x*(1-d^2)*d^2=1.92   ---- (B)

Dividing B by A

1-d^2=1.92/2=0.96

d^2=0.04, d=0.2=20%

Hence x=50 = exchange rate

Initial value for 1 USD = Rs 50

Loss = 2+1.92=3.92

Loss for Rs 100 = 3.92*2=7.84 also equal to % loss.

This problem is inappropriate at school or college level because it uses the term of points which is not usually taught at that level.