Advertisements
Advertisements
प्रश्न
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
उत्तर
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.
संबंधित प्रश्न
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.
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 value of a machine depreciates by 15% in the first year and by 12% in the second year. Find the value of the machine if its depreciation in the second year was Rs 1,632.
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.
What sum of money will amount to Rs 10,256.40 in 3 years at compound interest if the rates of interest for the successive years are 10%, 11% and 12%?
On what sum of money will the compound interest for 2 years at 10% p.a. compounded half-yearly amount to Rs 3,448.10?
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.
The compound interest on a certain sum of money at 10% p.a. for 3 years is Rs 4,965. What will be the simple interest on the same sum for 3 years at 11% p.a.?
The population of a city is 1,25,000. If the annual birth rate and death rate are 5.5% and 3.5% respectively. Calculate the population of the city after 3 years.
