the difference between simple and compund interest on a sum put out for 5 years at 3% was 46.80. Find the sum
please explain step by step
(answer : 5200)
Answers
Step-by-step explanation:
Given :-
The difference between simple and compund interest on a sum put out for 5 years at 3% was 46.80.
To find :-
Find the sum ?
Solution :-
Let the sum be Rs. X
Time (T) = 5 years
Rate of interest (R) = 3%
We know that
Simple Interest (S.I) = PTR/100
=> S.I = (X×5×3)/100
=> S.I = 15X/100
=> S.I = 3X/20
=> S.I = 0.15X
The Simple Interest for 5 years is
Rs.0.15X
We know that
Amount (A) = P[1+(R/100)]^n
=> A = X[1+(3/100)]⁵
=> A = X[(100+3)/100]⁵
=> A = X(103/100)⁵
We know that
Interest = Amount - Principle
=> Compound interest = X(103)/100)⁵-X
=> C.I = [(103)⁵X-(100)⁵X]/(100)⁵
=> C.I = (11592740743X-10000000000X)/(100)⁵
=> C.I = 1592740743X/(100)⁵
=> C.I = 1592740743X/10000000000
=> C.I = 0.1592740743X
=> C.I = 0.159X
(Correcting it upto three places )
The Compound Interest for 5 years is
Rs. 0.159X
Given that
The difference between simple and compund interest on a sum put out for 5 years at 3% was 46.80.
We have C.I = 0.159X and S.I = 0.15X
Difference = C.I - S.I
=> 0.159X - 0.15X = 46.80
=> 0.009X = 46.80
=> X = 46.80/0.009
=> X = (4680/100)/(9/1000)
=> X = (4680×1000)/(9×100)
=> X = 46800/9
=> X = 5200
Therefore, The sum = Rs. 5200
Answer:-
The required sum for the given problem is Rs. 5200
Used formulae:-
→ Simple Interest = PTR/100
→ Amount = P[1+(R/100)]^n
→ Amount = Principle + Interest
- P = Principle
- T = Time
- R = Rate of interest
- n = Number of times the interest is calculated compoundly.
Answer:
5200
Step-by-step explanation:
Given that the difference between simple and compund interest on a sum put out for 5 years at 3% was 46.80.
SI = (P × R × T)/100
Where R = 3%, T = 5 years and difference = Rs. 46.80
Let's say the principal is x.
SI = (x × 3 × 5)/100
SI = 15x/100
SI = 0.15x
CI = P(1 + R/100)^T - P
Substitute the values,
CI = x(1 + 3/100)⁵ - x
CI = x(103/100)⁵ - x
CI = x × 11592740743/10000000000 - x
CI = x × 0.159
CI = 0.159x
Now,
Difference = CI - SI
Substitute the values,
→ 46.80 = 0.159x - 0.15x
→ 46.80 = 0.009x
→ x = 46.80/0.009
→ x = 5200
Therefore, their sum is Rs 5200.