Simple & Compound interest problems (Guru level)

[hardikrs]

MBA chase, can you please explain this in detail. thanks

 

The compound interest on a certain sum for 2 year is Rs 832 and simple interest is Rs 800. Find the sum and the rate percent

Soluton: SI for one yr =400 , addition interest on 2nd yr = 32 rs. thus Interest on interest = 32 /400 = 8% now 8% of sum is 400 then sum is 5000.

[MBAchase]

MBA chase, can you please explain this in detail. thanks

 

The compound interest on a certain sum for 2 year is Rs 832 and simple interest is Rs 800. Find the sum and the rate percent

Soluton: SI for one yr =400 , addition interest on 2nd yr = 32 rs. thus Interest on interest = 32 /400 = 8% now 8% of sum is 400 then sum is 5000.

Dear Hardikrs,

one year SI is pr/100

If we calculate the CI for two yr the value of it is

P ( 1 +r/100)^2 - p = P(2r/100 + (r/100)^2)

 

and SI = 2PR/100

thus difference of CI and SI is p(r/100)^2 =(Pr/100)*(r/100)

thus so this is nothing but r% of 1st year interest or interest on interest.

so 1st yr interest is 400 and difference is 32 thus

r% of 400 is 32 thus r is 8%.

 

 

[MBAchase]

MBA chase, can you please explain this in detail. thanks

 

The compound interest on a certain sum for 2 year is Rs 832 and simple interest is Rs 800. Find the sum and the rate percent

Soluton: SI for one yr =400 , addition interest on 2nd yr = 32 rs. thus Interest on interest = 32 /400 = 8% now 8% of sum is 400 then sum is 5000.

Dear Hardikrs,

one year SI is pr/100

If we calculate the CI for two yr the value of it is

P ( 1 +r/100)^2 - p = P(2r/100 + (r/100)^2)

 

and SI = 2PR/100

thus difference of CI and SI is p(r/100)^2 =(Pr/100)*(r/100)

thus so this is nothing but r% of 1st year interest or interest on interest.

so 1st yr interest is 400 and difference is 32 thus

r% of 400 is 32 thus r is 8%.

and r is 8% i = 400 and t =1 thus P is 5000.

 

[Walter Immanual]

This is incorrect because the principal is reduced after the first payment. Here is how to solve it.

 

Let:

I1=interest paid in the first payment

I2=interest paid in the second payment

P1=principal paid in the first payment

P2=principal paid in the second payment

 

Because the payments are equal:

I1 + P1 = I2 + P2

 

Because all the principal is paid:

P1 + P2 = 550

 

First payment interest is on the full loan:

I1 = 550 x 0.2 = 110

 

Second payment interest is only on the remaining principal:

I2 = (550-P1) x 0.2

 

Substituting:

110 + P1 = (550 - P1)(0.2) + (550-P1)

110 + P1 = 110 - 0.2P1 + 550 - P1

2.2P1 = 550

P1 = 250

Payment = 250 + 110 = 360

 

Check:

P2 = 550 - P1 = 550 - 250 = 300

I2 = 0.2 x 300 = 60

Payment = 300 + 60 = 360

 

Paul

 

 

 

Hi i having confusion in this part

Second payment interest is only on the remaining principal:

I2 = (550-P1) x 0.2

 

because the calculation is based on C.I . The statment should be like this Second payment interest is only on the remaining principal:

I2 = (550-P1+110) x 0.2.........because the intrest of first year has to be added in to the 2nd year principle ammout