Advertisements
Advertisements
Question
On what sum will the difference between compound interest and the simple interest for 2 years at `7 1/2` % be Rs 22.50 ?
Advertisements
Solution
P = x ; t = 2 years ; r = `7 1/2` % = `15/2` %
For S.I. :
I = `("P" xx "r" xx "t")/100`
`= ("x" xx 15/2 xx 2)/100`
`= (3"x")/20`
For C.I. :
C.I. = `"P" (1 + "r"/100)^"t" - "P"`
`= "x" (1 + (15/2)/100)^2 - "x"`
`= "x" (1 + 15/(2 xx 100))^2 - "x"`
`= "x" (1 + 3/40)^2 - "x"`
= (x × 1.075 × 1.075) -x
= 1.15562S x - x
= 0.155625 x
Given C.I. - S.I. = Rs 22.50
⇒ 0.155625 x - `(3"x")/20 = "Rs" 22.50`
⇒ 0.155625 x - 0.15 x = Rs 22.50
⇒ 0.005625 x = Rs 22.50
⇒ x -Rs 4,000
Hence, sum = Rs 4,000
RELATED QUESTIONS
The simple interest on a certain sum in 2 years is Rs 1,300, whereas the compound interest on the same sum at the same rate and for the same time is Rs 1,365. Find the rate per cent and the sum.
Find the difference between the compound interest and the simple interest in 2 years on Rs 5,000 at 8% p.a. compounded annually.
Find the difference between the compound interest and the simple interest in 3 years on Rs 15,000 at 8% p.a. compounded yearly.
Anand borrows Rs 20,000at 9 % p.a. simple interest for 3 years. He immediately gave it to Prakash at `8 1/2 %` p.a. compound interest compounded annually.
Find Anand's loss or gain.
Calculate the amount and the compound interest for the following:
Rs 20,000 for 2 years if the rates of interest are `12 1/4` and `5 1/2` for the successive years.
Find the difference between the compound interest compounded yearly and half-yearly for the following:
Rs 20,000 for `1 1/2` years at 16 % p.a.
The population of a city is 1, 25,000. If the annual birth rate and death rate are 5.5% and 3.5% respectively, calculate the population of the city after 3 years.
The population of a city is 24,000. In the next 3 years it will be 27,783. Find the rate of growth of the population.
A mango tree was planted 3 years ago. The rate of growth is 20% per annum. If at present, the height of the tree is 1 m 8 cm, how high was it when planted?
A sum of money is lent out at compound interest for two years at 20% p.a., being reckoned yearly. If the same sum of the money was lent Gut at compound interest of the same rate of percent per annum C.I., being reckoned half yearly would have fetched Rs. 482 more by way of interest. Calculate the sum of money lent out.
