Welcome to Adda
My x a very industrious person, wants to establish his own unit . For this he need an instant loan of rs 5,00,000 and every five year he requires an additional loan of Rs. 100,000. if he had to clear all his outstanding in 20 years and he repays the principal of the firs loan equally over the 20 years, find what amount he would have to pay as interest on his initial borrowing if the rate of interest is 10%p.a. simple interest
He needs to clear the full amount within 20 years.
// He needs to repay the principal of the first loan equally over the 20 years//
Therefore, each year the principal should be reduced by 5,00,000/20=25000.
At the end of 1st year-
principal 5,00,000 and interest(10%)=50,000
At the end of 2nd year-
Principal 5,00,000-25000=4,75000 and interest(10%)=47500
.
.
At the end of 19th year-
Principal (50,000-25,000)=25,000 and interest= 2500
And at 20th year his loan gets cleared
Therefore, total interest=50,000 + 47500+.......2500+0
In AP
=20/2(50000+2500)
=5,25,000/-
Hope you got it now.
Cheers!
The additional loan has no significance in this question since the interest needs to be calculated on the initial loan.
The only thing Praneeth did wrong was the calculation of Principal and Interest and the end of 19th year which will be 5,000 and that of 20th year will be 2,500.
Rest well explained!!
Hi Praneet,
Could you please explain why did you reduce the principal by 25000? Need a bit detailed explanation to that step (500000/20 = 25000).
Praneeth if the interest is calculated on the subsequent amount each time would not be like Coumpound Interest?just asking.getting confused
Usha it is mentioned in the question that he repays the amount equally over the 20 years. So the amount gets reduced every month by 25000 and then the interest will be calculated accordingly
I didn't understand. What's there use of 1,00,000 in the question? Why 1L is not added every 5 years?
The question only wants to know the interest amount on the initial borrow of 5 Lakh.
1st Year: 5L*0.1
2nd Year: 4.75L*0.1
.
.
.
19th Year: 0.25*0.1
20th Year: 0*(0.1)
Total = 0.1*0.25(1+...+20)L = 0.1*0.25*(20*21*0.5 )L= 0.25*21 L = 5.25L = 525,000
The simple interest would be defined on the basis of the sum of the A.P.
50000 + 47500 + 45000 + .... + 2500 = 525000
Initial borrowing = Rs 5,00,000
Rate of interest = 10% p.a.
Time = 20 years
Interest = P*T*R/100 = 500000*20*10/100 = Rs 10,00,000
