Advertisements
Advertisements
Question
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.
Advertisements
Solution
Let the principal be ₹ 100
For first case r = 20% p.a.
n = 2 years
A = P`(1 + r/100)^n`
= ₹ 100`(1 + 20/100)^2`
= ₹ 100`(1 + 1/5)^2`
= ₹ 100`(6/5)^2`
= ₹ `(100 xx 6 xx 6)/(5 xx 5)`
= ₹ `(3,600)/(25)`
= ₹ 144
∴ C.I. = A - P
= ₹ 144 - ₹ 100
= ₹ 44
For second case
r = 20% p.a. = `(20)/(2)`% half yearly = 10% semi annual
Time = 2 years = 4 half years
A = P`(1 + r/100)^n`
= ₹100`(1 + 10/100)^4`
= ₹100`(1 + 1/10)^4`
= ₹100`(11/10)^4`
= ₹`(100 xx 11 xx 11 xx 11 xx 11)/(10 xx 10 xx 10 xx 10)`
= ₹`(121 xx 121)/(10 xx 10)`
= ₹`(14,641)/(100)`
= ₹ 146·41
C.I. = A - P
= 146·41 - 100
= ₹ 46·41
Difference between two interest
= ₹ 46·41 - ₹ 44·00
= ₹ 2·41
If difference is ₹2·41 then principal be ₹100
If difference is ₹482 then principal will be
= ₹ `(100)/(2·41) xx 482`
= ₹ `(100 xx 482)/(241) xx 100`
= ₹ 100 x 100 x 2
= ₹ 20,000
∴ Sum is ₹ 20,000
RELATED QUESTIONS
Find the difference between the compound interest and the simple interest in 3 years on Rs 15,000 at 8% p.a. compounded yearly.
Calculate the Amount and Cornpound Interest for the Following, when Cornpounded Annually:
Rs 12,000 for 3 years at 15 % p.a.
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.
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.
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,
0/o per annum 1, 15,200. If it increases at the rate of `6 2/3` % per annum find
Its population 2 years ago.
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 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.?
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?
Find the difference between the simple interest and compound interest on 2,500 for 2 years at 4% p.a., compound interest being reckoned semi-annualy.
