Banking difficult problem solution

The difference between compound and simple interest on a certain sum for 2 years is 7½ % per annum is Rs 360. Find the sum .Verify the answer.

• Interpretation of the problem:
  

1.Knowledge of the difference between compound and simple interest.
2.Knowledge of the formula's for compound and simple interest.
3.Identifing the terms giving in the problem.

• Different approches to solve the problem:
  

1.using formula.

• Concept used:

identifing the values from the given data. R=7½% , n-2 years
Assumping that principal P=Rs 100.$Insertformulahere$ Identifing the suitable formula, i.e A=P
$S.I=PTR/100$
Substitution: consider $S.I=PTR/100$( sustitute the values)
$S.I={\frac {100X2X15}{2X100}}$ ( on simplification)
S.I = Rs 15.
With compound interest ;$A=P[1+{\frac {R}{100}}]^{n}$
A =$100[{\frac {200+15}{200}}]^{2}$
=$100[{\frac {215}{200}}]^{2}$100
=$100X{\frac {215}{200}}X{\frac {215}{200}}$
A= Rs 115.562
C.I = Rs 115.562- 100
C.I = Rs 15.562
The difference in C.I and S.I is Rs 0.56
The difference in C.I and S.I is Rs 0.56 when principal=Rs 100.
If the difference in C.I and S.I is Rs 360, principal = x 360 = Rs 64285.
Verification :
$S.I={\frac {PTR}{100}}$
$S.I={\frac {64285X2X7.5}{100}}$
= Rs 9642.75 $A=P[1+{\frac {R}{100}}]^{n}$
A=P= 64285[1+{\frec}{7.5}{100}}]^2= 74289.3
C.I = A – P
= 74289.3- 64285
= 10004.3 Rs
Therefore the difference between C.I and S.I is = Rs 360. [Banking_click]