If simple interest and compound interest of a certain sum of money for two years are ₹8400 and ₹8652, then let us write by calculating the sum of money and the rate of interest.
Answers
Answer:
70000, 6%
Step-by-step explanation:
let the principal be talking P
and rate of interest be r % p. a
Time = 2 yr
Given :-
If the simple intrest and compound interest of of certian sum of money for two years are RS. 8400 and RS. 8652
To Find :-
Sum of money
Rate
Solution :-
Let the principal be p
And rate be r
SI = PRT/100
SI = p × r × 2/100
SI = 2pr/100(1)
Now
CI = P{(1 + r/100)ⁿ - 1}
CI = p{(1 + r/100)² - 1}
CI = p{1 + 2r/100 + r²/(100)² - 1}
CI = p{1 - 1 + 2r/100 + r²/100²}
CI = p{2r/100 + r²/100²}
Taking 100 and r as common
CI = pr/100(2 + r/100) (2)
Now We may divide both equations
{pr/100(2 + r/100)}/{2pr/100} = 8652/8400
{2 + r/100}/{2/100} = 4326/4200
{2 + r/100} = 4326/4200 × 2
r/100 = 4326/2100 - 2
r/100 = 4326 - 4200/2100
r/100 = 126/2100
r = 126/2100 × 100
r = 12600/2100
r = 6%
Now
Using 1
8400 = p × r × 2/100
8400 = p × 6 × 2/100
8400 = p × 12/100
8400 = p × 3/25
8400 × 25/3 = p
2800 × 25 = p
70000 = p