Advertisements
Advertisements
Question
Mr. Sharma borrowed a certain sum of money at 10% per annum compounded annually. If by paying Rs.19,360 at the end of the second year and Rs. 31,944 at the end of the third year he clears the debt; find the sum borrowed by him.
Advertisements
Solution
At the end of the two years the amount is
`"A"_1 = "P"( 1 + r/100 )^n`
⇒ `"A"_1 = "P"( 1 + 10/100 )^2`
Mr. Sharma paid Rs. 19,360 at the end of the second year.
So for the third year the principal is A1 - 19,360.
Also, he cleared the debt by paying Rs. 31,944 at the end of the third year.
`"A"_2 = "P"( 1 + r/100 )^n`
⇒ 31,944 = `("P"( 1 + 10/100 )^2 - 19,360)( 1 + 10/100)^1`
⇒ 29040 = `("P"( 1 + 10/100 )^2 - 19,360)`
⇒ `"P"( 1 + 10/100 )^2 = 48,400`
⇒ P = Rs. 40,000
Mr. Sharma borrowed Rs. 40,000.
APPEARS IN
RELATED QUESTIONS
The cost of a machine is supposed to depreciate each year at 12% of its value at the beginning of the year. If the machine is valued at Rs. 44,000 at the beginning of 2008, find its value :
(i) at the end of 2009.
(ii) at the beginning of 2007.
According to a census taken towards the end of the year 2009, the population of a rural town was found to be 64,000. The census authority also found that the population of this particular town had a growth of 5% per annum. In how many years after 2009 did the population of this town reach 74,088 ?
A sum of money, invested at compound interest, amounts to Rs. 16,500 in 1 year and to Rs. 19,965 in 3 years. Find the rate per cent and the original sum of money invested.
A sum of money lent out at C.I. at a certain rate per annum becomes three times of itself in 10 years. Find in how many years will the money become twenty-seven times of itself at the same rate of interest p.a.
The difference between compound interest for a year payable half-yearly and simple interest on a certain sum of money lent out at 10% for a year is Rs. 15. Find the sum of money lent out.
Find the amount and the compound interest payable annually on:
Rs.16000 for 2 years at 15% and 12% for the successive years.
Find the amount and compound interest on Rs.7500 for 1`(1)/(2)` years at 8%, payable semi-annually.
In what time will Rs 15625 amount to Rs 17576 at 4% p.a. compound interest?
In how many years will Rs 2000 amount to Rs 2662 at 10% p.a. compound interest?
At what rate percent will Rs.12000 yield Rs.13891.50 as compound interest in 3 years?
