Question

If the difference between the Compound interest and simple interest on a sum
of 5% rate of interest per annum for three years is Rs.36.60, then the sum is​

Answer 1

Answer:

answer for the given problem is given

Answer 2

Answer:

If the difference between the Compound interest and simple interest on a sum of 5% rate of interest per annum for three years is Rs.36.60, then the sum is​ Rs. 4800.

Step-by-step explanation:

According to the question,

(Compound Interest - Simple Interest) = 36.60....... eq. 1
This is the main equation of the problem.

Now let us simplify the formula to avoid difficulty and possible errors

Given,
Tenure of the interest (time, t) = 3 years
Rate of both S.I. and C.I. = 5%

∴ For simple interest,
The formula for calculating S.I. $= \frac{p \times r \times t}{100}$
where p is the principal sum.
∵ r = 5%, and, t = 3 yrs.,

∴ $S.I. = \frac{p \times 5 \times 3}{100} = \frac{3p}{20}$ .............. (2)

∴ For compound interest,
The formula for calculating C.I. $= p[(1 + \frac{r}{100})^{n} - 1]$
where p is the principal sum.
∵ r = 5%, and, n (time)= 3 yrs.,
∴ $C.I. = p[(1 + \frac{5}{100})^{3} - 1]$

⇒ $C.I. = p[(1 + \frac{1}{20})^{3} - 1]$

⇒ $C.I. = p[( \frac{21}{20})^{3} - 1]$

⇒ $C.I. = p[( \frac{9261}{8000} - 1]$

⇒ $C.I. = p[ \frac{9261 - 8000}{8000}]$

⇒ $C.I. = p[ \frac{1261}{8000}]$................ (3)

Now, substituting the value of (2) and (3) in the main equation, i.e., eq. 1, we get,

(3) - (2)
$\frac{1261p}{8000}- \frac{3p}{20}= 36.60$

⇒ $\frac{1261p}{8000}- \frac{3p}{20}= \frac{3660}{100}$

⇒ $\frac{1261p - 1200p}{8000}= \frac{3660}{100}$

⇒ $\frac{61p}{8000}= \frac{3660}{100}$

⇒ $\frac{61p}{80} = 3660$

⇒ $61p = 3660 \times 80$

⇒ $p = \frac{3660 \times 80}{61}$

⇒ $p = 60 \times 80 = 4800$

Conclusion:
The principal amount is Rs. 4800.

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