Advertisements
Advertisements
Question
A sum of money placed at compound interest compounded annually amounts to Rs 31,360 in 2 years and to Rs 35,123.20 in 3 years. Calculate the rate of interest and the sum.
Solution
P = x ; r = ? ; t= 2 and 3 years ; A = Rs 31,360 ( 2 years) and Rs 35, 123.20 ( 3 years)
`"A" = "P" (1 + "r"/100)^"n"`
`31360 = x (1 + "r"/100)^2` .........(i)
`35123.20 = "x" (1 + "r"/100)^3` ..............(ii)
`therefore ("x" (1 + "r"/100)^3)/(x (1 + "r"/100)^2) = 35123.20/31360`
⇒ `(1 + "r"/100) = 35123.20/31360`
⇒ `"r"/100 = 35123.20/31360 - 1`
⇒ `"r"/100 = (35123.20 - 31360)/31360`
`"r" = 3763.20/31360 xx 100`
r = 12%
Using (i)
`"x" (1 + "r"/100)^2` = Rs 31,360
`"x" (1 + 12/100)^2` = Rs 31,360
`"x" (112/100)^2` = Rs 31,360
1 .2544 X = Rs 31,360
x = Rs 25,000
The sum = Rs 25,000 and rate of interest = 12 %.
APPEARS IN
RELATED QUESTIONS
Amita wanted to start a business for which she needed Rs, 40000. She borrowed this from Dolly at 10% p.a compounded semi-annually. Find the extra amount that she needs to pay at the end of two years to clear her debt.
Pradeep gave Rs.16000 to a friend for 1.5 years at 15% p.a. compounded semi-annually. Find the interest earned by him at the end of 1.5 years.
Manoj borrowed Rs 25,000 from Sohan at 8.4 % p.a. compound interest. After 2 years Manoj cleared Rs 17,500 and a motorcycle. Find the cost of the motorcycle.
The cost of a scooter depreciated by Rs 5100 during the second year and by Rs 4,335 during the third year. Calculate
The original cost of the scooter.
The cost of a scooter depreciated by Rs 5100 during the second year and by Rs 4,335 during the third year. Calculate
Calculate the amount and cornpound interest of the following, when cornpounded annually:
Rs 20,000 for 2 years at `12 1/2` % p.a.
Calculate the amount and the compound interest for the following:
Rs 12,500 for 3 years if the rates for the successive years are 8%, 9% and 10% respectively.
Calculate the amount and the compound interest for the following:
Rs 10,000 for 3 years if tl1e rates of interest are 10%, 11% and 12% for the successive years.
A sum of money placed at compound interest compounded annually amounts to Rs 47,610 in 2 years and to Rs 54,751.50 in 3 years. Calculate the rate of interest and the sum.
A sum of money placed at compound interest compounded annually amounts to Rs 26,460 in 2 years and to Rs 29,172.15 in 4 years. Calculate the rate of interest and the sum.
