Advertisements
Advertisements
Question
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.
Solution
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
APPEARS IN
RELATED QUESTIONS
Ranbir borrows Rs. 20,000 at 12% per annum compound interest. If he repays Rs. 8400 at the end of the first year and Rs. 9680 at the end of the second year, find the amount of loan outstanding at the beginning of the third year.
Calculate the amount and the compound interest for the following:
Rs.30,000 at 8°/o p.a. in `2 1/2` years
Calculate the amount and the compound interest for the following:
Rs.10,000 at 8°/o p.a. in `2 1/4` years
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.
Nikita invests Rs.6,000 for two years at a certain rate of interest compounded annually. At the end of first year it amounts to Rs.6,720. Calculate:
(a) The rate of interest.
(b) The amount at the end of the second year.
Calculate the amount and compound interest on Rs 20000 for 3 years at 10% per annum, interest being payable annually.
A man invests Rs 24000 for two years at compound interest, If his money amounts to Rs 27600 after one year, find the amount at the end of second year.
Find the amount and the compound interest on Rs 17500 for 3 years, if the rates for successive years is 4%, 5% and 6% respectively, the interest is payable annually.
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.
