Problem Solving

The problem is:
Ram lends a sum of money to Shyam at an interest rate of 5% p.a.
After 2 years, he charges an interest of 8% p.a
At the end of 5 years, Shyam pays Rs. 13400 to Ram
How much money did he initially borrow?

A. Rs.8000
B. Rs. 9000
C. Rs. 10000
D. Rs. 10500

The correct answer is: C

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And I approached this problem by using A=A1+A2, with A: total amount of money which include both the principal and the interest, received after 5 years. A1: total amount of money received after 2 first years. A2: total amount of money received after next 3 years.


And what I have according to this equation:
A = A1 + A2 (A=P+I, with P: principal that needs answered, I: interest received after each period)
13400 = 11p/10 + 124p/100
13400= 234P/100
P= 5726.50

According to the multiple choices the problem challenges the testees to choose, I haven't made the right method of solution.

Actually to get answer C, the equation should be: (After 5 years, the amount of money which includes both of principal and interest)
A = P+(I1+I2) with I: interest received after each period. I1: after first 2 years. I2: after next 3
13400 = P (p/10 + 24p/100)
P = 10000.

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My question is: What needs to be explained and correctly understood to get the latter equation for the correct answer C


I was learning GMAT by myself. I really need help from GMAT geeks here.
Thanks for your reading my post. Hope you have a great day.

Cheers,
Amu

It looks like this:

Loan * (1 + interest 1st year + interest 2nd year + interest 3rd year + interest 4th year + interest 5th year)

=

x * (1 + .05 + .05 + .08 + .08 + .08)

=

x * (1.34)

So 1.34x = 13400, and x = 10000.