Advertisements
Advertisements
Question
The difference between the compound interest and simple interest on a certain sum at 15% per annum for 3 years is Rs 283.50. Find the sum.
Advertisements
Solution
Given:
CI - SI = Rs 283 . 50
R = 15 %
n = 3 years
Let the sum be Rs x.
We know that:
\[A = P(1 + \frac{R}{100} )^n \]
\[ = P(1 + \frac{R}{100} )^n \]
\[ = x(1 + \frac{15}{100} )^3 \]
\[ = x \left( 1 . 15 \right)^3 . . . (1)\]
Also,
\[SI = \frac{PRT}{100} = \frac{x(15)(3)}{100} = 0 . 45 x\]
\[A = SI + P = 1 . 45x . . . (2)\]
Thus, we have:
\[x \left( 1 . 15 \right)^3 - 1 . 45x = 283 . 50 \][From (1) and (2)]
\[1 . 523x - 1 . 45x = 283 . 50\]
\[0 . 070875x = 283 . 50\]
\[x = \frac{283 . 50}{0 . 070875}\]
\[ = 4, 000\]
Thus, the sum is Rs 4, 000.
RELATED QUESTIONS
Find the compound interest on Rs 160000 for one year at the rate of 20% per annum, if the interest is compounded quarterly.
In a factory the production of scooters rose to 46305 from 40000 in 3 years. Find the annual rate of growth of the production of scooters.
The population of a certain city was 72000 on the last day of the year 1998. During next year it increased by 7% but due to an epidemic it decreased by 10% in the following year. What was its population at the end of the year 2000?
The production of a mixi company in 1996 was 8000 mixies. Due to increase in demand it increases its production by 15% in the next two years and after two years its demand decreases by 5%. What will be its production after 3 years?
Pritam bought a plot of land for Rs 640000. Its value is increasing by 5% of its previous value after every six months. What will be the value of the plot after 2 years?
Sameerrao has taken a loan of ₹ 12500 at a rate of 12 p.c.p.a. for 3 years. If the interest is compounded annually, then how many rupees should he pay to clear his loan?
Find the difference between simple interest and compound interest on ₹ 20000 at 8 p.c.p.a.
Find the amount and the compound interest on ₹ 4,000 in 2 years, if the rate of interest for the first year is 10% and for the second year is 15%.
The cost of a sewing machine is Rs 7,000. Its value depreciates at 8% p.a. Then the value of the machine after 2 years is Rs 5,924.80.
The value of a car, bought for Rs 4,40,000 depreciates each year by 10% of its value at the beginning of that year. So its value becomes Rs 3,08,000 after three years.
