Advertisements
Advertisements
प्रश्न
A certain sum of money invested at compound interest compounded annually amounted to Rs 26,450 in 2 years and to Rs 30,417.50 in 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 26,450 in 2 vears and Rs 30,417.50 in 3 years.
`"A" = "P" (1 + "r"/100)^"n"`
`26450 = "x" (1 + "r"/100)^2` ........(i)
`30417.50 = "x" (1 + "r"/100)^3` ........ (ii)
Dividing (ii) by (i)
`("x" (1 + "r"/100)^3)/("x" (1 + "r"/100)^2) = 30417.50/26450`
`=> 1+ "r"/100 = 30417.50/26450`
`=>"r"/100 = 30417.50/26450 -1`
`=>"r"/100 = (30417.50 - 26450)/26450`
`=>"r"/100 = 3967.50/26450`
`=> "r" = 3967.50/26450 xx 100`
⇒ r = 15 %
using (i)
`"x" (1 + "r"/100)^2 = Rs 26450`
`"x" (1 + 15/100)^2` = Rs 26450
`"x" xx 23/20 xx 23/20` = Rs 26450
`"x" xx 529/400` = Rs 26450
`"x" = "Rs" (26450 xx 400)/529`
x = Rs 20,000
Hence, rate of interest= 15 % and sum invested =Rs 20,000
संबंधित प्रश्न
Mr Lalit invested Rs. 5000 at a certain rate of interest, compounded annually for two years. At the end of the first year, it amounts to Rs. 5325. Calculate
1) The rate of interest
2) The amount at the end of the second year, to the nearest rupee.
Nikita invests Rs. 6000 for two years at a certain rate of interest compounded annually. At the end of the first year, it amounts to Rs. 6720. Calculate:
- the rate of interest.
- the amount at the end of the second year.
The value of a machine depreciates by 10%, 12% and 15% in the first 3 years. Express the total depreciation of the machine as a single per cent during the three years.
Anuj and Rajesh each lent the same sum of money for 2 years at 8% simple interest and compound interest respectively. Rajesh received Rs. 64 more than Anuj. Find the money lent by each and interest received.
A sum of money is invested at 10% per annum compounded half yearly. If the difference of amounts at the end of 6 months and 12 months is Rs.189, find the sum of money invested.
How much will Rs 14000 amounts to 2 years at compound interest, if the rates for the successive years be 5% and 8% respectively?
Find the difference between the compound interest and simple interest on Rs 20,000 at 12% per annum for 3 years, the compound interest being payable annually.
The value of a mobile depreciated by 5% per year during the first two years and 10% per year during the third year. Express the total depreciation of the value of the mobile in percent during the three years.
A man borrows Rs.20000 at 10% per annum compound interest payable annually. If he repays Rs.5000 at the end of the first year and Rs.10000 at the end of the second year; how much should he pay at the end of the third year in order to clear the account? Find the answer correct to the nearest rupee.
Priyanka lends Rs.15,500 at 10% for the first year, at 15% for the second year and at 20% for the third year. If the rates of interest are compounded yearly, find the difference between the compound interest of the second year and the third year.
