Advertisements
Advertisements
Question
A certain sum of money invested at compound interest compounded annually amounted to Rs 5,082 after 2 years and to Rs 5,590.20 after 3 years. Calculate the rate of interest and the sum invested.
Advertisements
Solution
Here, r =? P = x (say)
T = 2 years and 3 years
A= Rs 5,082 in 2 years and Rs 5,590.20 in 3 years.
` "A" = "P" (1 + "r"/100)^"n"`
`5082 = "x" (1 + "r"/100)^2 ` .................. (i)
`5590.20 = "x" (1 + "r"/100)^3` ................(ii)
Dividing (ii) by (i)
`("x" (1 + "r"/100)^3)/("x" (1 + "r"/100)^2) = 5590.20/5082`
`=> 1 + "r"/100 = 5590.20/5082`
`=> "r"/100 = 5590.20/5082 - 1`
`=> "r"/100 = (5590.20 - 5082)/5082`
`=> "r"/100 = 508.20/5082`
`=> "r" = 508.20/5082 xx 100`
⇒ r = 10%
using (i)
`"x" (1 + "r"/100)^2 = "Rs" 5082`
`"x" (1 + 10/100)^2 = "Rs" 5082`
`"x" xx 11/10 xx 11/10 = "Rs" 5082`
`"x" xx 121/100 = "Rs" 5082`
`"x" = "Rs" (5082 xx 100)/121`
x = Rs 4200
Hence, rate of interest= 10°10 and sum invested =Rs 4,200.
RELATED QUESTIONS
Rajeev borrowed Rs 15,000 from Sanjay at 12% p.a. compound interest. After 2 years Rajeev gave Rs 7,500 and a scooter to clear the account. Find the cost of the scooter.
What sum of money will amount to Rs 7,128 in 2 years at compound interest, if the rates of interest are 8% and 10% for successive years?
The cost of a scooter depreciated by Rs 5100 during the second year and by Rs 4,335 during the third year. Calculate
the rate of depreciatlon
The cost of a machine depreciated by Rs 2592 during the third year and by Rs 2332.80 during the fourth year. Calculate :
The original cost.
The cost of a machine dep reciated by Rs 2592 during the third year and by Rs 2332.80 during the fourth year. Calculate :
The cost at the end of the fourth year.
Calculate the amount and cornpound interest for the following, when cornpounded annually:
Rs 16,000 for 3 years at `7 1/2` % p.a.
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.
On what sum of money will the compound interest for 2 years at 8% per annum amount to Rs 1399.68?
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.
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.
