A money lender borrows money at 6 % per annum and pays the interest at the end of the year. He lends it at 8% per annum compounded half yearly and receives the interest at the end of the year. In this way, he gains Rs 172.8 a year. The amount of money he borrows is
A) Rs. 7000
B) Rs. 7500
C) Rs. 8000
D) Rs.7800
E) None of these
Answers
Answer:
Amount of money borrowed = C) - Rs. 8000
Step-by-step explanation:
Let the amount of mney borrowed = X
He is borrowing the money at 6%per annum.
∴ Interest paid by him = X × 6%
∴ Interest paid = 0.06X ....... (1)
When he is lending the money, he is charging 8% per annum compounded half yearly.
∴ Rate of interst for 6 months = 8/2 = 4%
Interst gained per year = X (1 + 4%)^2 - X
∴ Compounded interst gained in one year = X × 1.04² - X
∴ Compounded interst gained in one year = 1.0816X - X
∴ Compounded interst gained in one year = 0.0816 X
Amount gained per year = Interest gained - Interestpaid
∴ Amount gained per year = 0.0816X - 0.06X = 0.0216X
But this amount is give as rs. 172.8
∴ 172.8 = 0.0216X
∴ X = 172.8 / 0.0216
∴ X = Rs. 8000
Amount of money borrowed = C) - Rs. 8000
Answer:
Rs 8000
Option C
Step-by-step explanation:
A money lender borrows money at 6 % per annum and pays the interest at the end of the year. He lends it at 8% per annum compounded half yearly and receives the interest at the end of the year. In this way, he gains Rs 172.8 a year. The amount of money he borrows is
A) Rs. 7000
B) Rs. 7500
C) Rs. 8000
D) Rs.7800
E) None of these
Let say Money borrowed = Rs X
SImple interest = P * r * t /100
r = 6% per annum , t = 1year P = Rs X
6% interest paid = X * 6 * 1 /100 = 0.06x
Compound Interest = P (1 + r/100n)^nt - P
P = rs X , r = 8% per annum n =2 ( twice in a year) t = 1 Year
= X (1 + 8/(100*2))^(2*1) - X
= X(1.04)^2 - X
=X(1.0816) -X
= 0.0816X
Earning 0.0816X - 0.06X = 0.0216X
0.0216X = 172.8
=> X = 8000
The amount of money he borrows = Rs 8000
option C is correct