Advertisements
Advertisements
Question
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.
Advertisements
Solution
P=Rs 20,000; t = `1 1/2` years
When compounded yearly: r = 16% p.a.
`"A" = "P" (1 + "r"/100)^"n"`
A = Rs 20000 `(1 + 16/100)(1 + 16/100)^(1/2)`
= Rs 20000 × 1.16 × `(1 + 1/2 xx 16/100)`
= Rs 20, 000 x 1.16 x 1.08
= Rs 25,056
C.I. = A - P
= Rs (25,056 - 20,000)
= Rs 5,056
When compounded half-yearly:
`"A" = "P" (1 + "r"/100)^"n"`
A = Rs 20000 `(1 + 8/100)^3`
= Rs 20,000 x 1.08 x 1.08 x 1.08
= Rs 25,194.24
C.l. = A - P
= Rs (25,194.24- 20,000)
= Rs 5,194.24
Hence the difference in the interest=Rs (5,194.24 - 5,056) = Rs 138.24
RELATED QUESTIONS
Find the difference between the compound interest and the simple interest in 2 years on Rs 5,000 at 8% p.a. compounded annually.
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.
Meera borrowed Rs 35,000 at 12.5% p.a. simple interest for 3 years. She immediately gave it to Archana at 12 % p.a. compound interest compounded annually. Find Meera's loss or gain at the end of 3 years.
Find the difference betlween the compound interest compounded yearly and half-yearly for the following:
Rs 15,000 for `1 1/2` years at 12 % p.a.
In a factory the production of scooters rose to 46,305 from 40,000 in 3 years. Find the annual rate of growth of the production of scooters.
The present population of a town is 1, 15200.If it increases at the rate of `6 2/3`% per annum , find
Its population after 2 years
A machine was purchased 2 years ago. Its value decreases by 10% every year. Its present value is Rs 19,083.60. For how much money was the machine purchased?
Under the electrification programme of villages, the number of villages with electricity rose to 27,040 from 25,000 in 2 years. Find the rate of growth in the number of villages with electricity.
The value of a property decreases every year at the rate of 5%. If its value at the end of 3 years be Rs 44,540, what was the original value at the beginning of these 3 years?
Find the Compound Interest on Rs. 2,000 for 3 years at 15% per annum Compounded annually.
