A certain sum was put on simple interest at 20% per annum for 2 years. then the amount received after 2 years put on compound inte

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1. Step-by-step explanation:

   Given:–

   A certain sum was put on simple interest at 20% per annum for 2 years. then the amount received after 2 years put on compound interest 15% per annum for 2 more years. if the amount received at the end of 4 year is 34450.

   To find:–

   Find the amount invested?

   Solution:–

   Let the amount be invested = Rs. P

   Principle = Rs. P

   Rate of Interest (I) = 20%

   Time (T)=2 years

   We know that Simple Interest (I) = PTR/100

   =>I = (P×2×20)/100

   =>I = 40P/100

   =>I = 2P/5

   Simple Interest after two years = Rs. 2P/5

   Amount = Principle+ Interest

   =>Amount = P+(2P/5)

   =>Amount = (5P+2P)/5

   Amount = Rs. 7P/5

   Then if it is invested again then

   Principle (P) =Rs. 7P/5

   Rate of interest (R)=15%

   Time (T)=2 years

   Number of times the compound interest is calculated (n)=2 years

   We know that

   Amount (A) = P[1+(R/100)]^n

   =>A = (7P/5)[1+(15/100)]^2

   =>A = (7P/5)[1+(3/20)]^2

   =>A = (7P/5)[(20+3)/20]^2

   =>A = (7P/5)×(23/20)^2

   =>A = (7P/5)×(23/20)×(23/20)

   =>A = (7P×23×23)/(5×20×20)

   =>A = 3703P/2000

   Amount received at the end of 4 years

   = Rs. 3703P/2000

   According to the given problem

   Amount received at the end of 4 years

   =Rs.34450

   =>3703P/2000 = 34450

   =>3703P = 34450×2000

   =>3703P = 68900000

   =>P = 68900000/3703

   =>P = 18606.535…

   =>P = Rs. 18606.54

   Answer:–

   The Amount invested for the given problem is

   Rs . 18606.54

   used formulae:–

   • Simple Interest (I) = PTR/100

   • Amount = Principle+ Interest

   • Amount (A) = P[1+(R/100)]^n

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