Explanation:
Given :-
A person borrows a certain amount from a bank for 3 years at a rate of 7% compound interest annually. And he paid 785966 as total interest.
To find :-
What was the amount borrowed?
Solution :-
Let the principle be Rs. P
Time (T) = 3 years
Rate of Interest (R) = 7%
If the interest calculated compoundly per annum
then n = 3
Compound Interest (CI) = Rs. 785966
We know that
A = P[1+(R/100)]^n
On substituting these values in the above formula then
=> A = P[1+(7/100)]³
=> A = P[(100+7)/100]³
=> A = P(107/100)³
=> A = P(107×107×107)/(100×100×100)
=> A = P (1225043/1000000)
=> A = 1225043P/1000000 ----------(1)
We know that
Amount = Principle + Interest
Equation (1) becomes
=> P+785966 = 1225043P/1000000
=> (P+785966)×1000000 = 1225043P
=> 1000000P + 785966000000 = 1225043P
=> 1225043P-1000000P = 785966000000
=> 225043P = 785966000000
=> P = 785966000000 / 225043
=> P = 3492514.7638451
=> P = 3492514.76
Answer:-
The money borrowed by the man from the bank is Rs. 3492514.76
Used formulae:-
→ A = P[1+(R/100)]^n
→ Amount = Principle + Interest
P = Principle
T = Time
R = Rate of Interest
n = Number of times the interest calculated compoundly per annum