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
APPEARS IN
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.
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.
On what sum will the difference between compound interest and the simple interest for 2 years at `7 1/2` % be Rs 22.50 ?
On what sum will the difference between compound interest and the simple interest for 3 years at 12% be Rs 1,123.20?
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?
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.
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.
A new car is purchased for Rs 4, 00,000 .Its value depreciates at the rate of 10% per annum. What will be its value after 4 years?
A building worth Rs 1, 33,100 is constructed on a plot of land worth Rs 72,900. After how many years will the values of both be same, if the land appreciates at 10% p.a. and the building depreciates at 10% p.a.?
The cost of a T.V. was quoted Rs 17,000 at the beginning of the year 1999. In the beginning of 2000 the price was hiked by 5%. Because of decrease in demand the cost was reduced by 4% in the beginning of 2001. What is the cost of the T.V. in 2001?
