Total compound interest on a certain sum (compound annually) for 2 year is Rs. 234 and for 3 year is Rs. 381. find the rate of interest.
Answers
Answer:
50/3 % Per annum
Step-by-step explanation:
Total compound interest on a certain sum (compound annually) for 2 year is Rs. 234 and for 3 year is Rs. 381. find the rate of interest.
Let say Amount = P
rate of interest = 100R
Interest for 2 years = P (( 1 + 100R/100)² - 1) = P (( 1 + R)² - 1) = 234
Interest for 3 years = P (( 1 + 100R/100)³ - 1) = P (( 1 + R)³ - 1) = 381
=> P (( 1 + R)³ - ( 1 + R)²) = 147
=> P(1+R)²R = 147 eq 1
P (( 1 + R)² - 1) = 234
=> PR(2 + R) = 234 eq2
eq 2 /Eq 1
=> PR(2 + R) = 234
(2 + R)/(1 + R)² = 234/147
=> 294 + 147R = 234 + 234R² + 468R
=> 234R² + 321R - 60 = 0
=> 78R² + 107R - 20 = 0
=> 78R² -13R + 120R - 20 = 0
=> 13R(6R - 1) + 20(6R -1) = 0
=> R = 1/6
100R = 100/6 = 50/3 % Per annum
Additional Info :
P = Rs 648
1st year 108
2nd Year 126
3rd Year 147