Chit Calculator finding amount taken, finding Rate of intrest.

Chit Fund Calculator

Chit Amount (P):

Total Period (in months):

Chit Sequence Number:

Rate of Interest per Month (r):

Calculate Amount Taken (x)

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Amount Taken (x):

Calculate Rate of Interest per Month (r)

Definitions and Formulas:

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Definitions and Formulas:

• ChitAmount (P): The total amount invested in the chit.
• Amount Taken (x): The amount taken after action.
• Interest on Amount Taken: $(x * t * r) / 100$, where:
  • $t$ = Total period in months - Chit sequence number
  • $r$ = Rate of interest per month

The formula provided is: $P = x + \frac{x \cdot t \cdot r}{100}$

This can be rewritten as: $P = x \left(1 + \frac{t \cdot r}{100}\right)$

Given any of these variables, we can solve for the unknowns.

Problem 1: Finding Amount Taken (x)

Given:

• ChitAmount ($P$)
• Chit sequence number
• Total period ($t_{total}$)
• Rate of interest per month ($r$)

Let's define:

• $t = t_{total} - \text{Chit sequence number}$

The formula is: $P = x \left(1 + \frac{t \cdot r}{100}\right)$

Solving for $x$: $x = \frac{P}{1 + \frac{t \cdot r}{100}}$

Problem 2: Finding Rate of Interest per Month (r)

Given:

• ChitAmount ($P$)
• Amount Taken ($x$)
• Chit sequence number
• Total period ($t_{total}$)

Let's define:

• $t = t_{total} - \text{Chit sequence number}$

The formula is: $P = x \left(1 + \frac{t \cdot r}{100}\right)$

Solving for $r$: $\frac{P}{x} = 1 + \frac{t \cdot r}{100}$ $\frac{P}{x} - 1 = \frac{t \cdot r}{100}$ $r = \left( \frac{\frac{P}{x} - 1}{t} \right) \cdot 100$

Example Calculations

1. Finding Amount Taken (x):

   • Suppose ChitAmount ($P$) = 100,000
   • Chit sequence number = 3
   • Total period = 12 months
   • Rate of interest per month ($r$) = 2%

   First, calculate $t$: $t = 12 - 3 = 9$

   Then, find $x$: $x = \frac{100,000}{1 + \frac{9 \cdot 2}{100}} = \frac{100,000}{1 + 0.18} = \frac{100,000}{1.18} \approx 84,746.61$

2. Finding Rate of Interest per Month (r):

   • Suppose ChitAmount ($P$) = 100,000
   • Amount Taken ($x$) = 85,000
   • Chit sequence number = 3
   • Total period = 12 months

   First, calculate $t$: $t = 12 - 3 = 9$

   Then, find $r$: $\frac{100,000}{85,000} = 1 + \frac{9 \cdot r}{100}$ $1.1765 = 1 + \frac{9 \cdot r}{100}$ $0.1765 = \frac{9 \cdot r}{100}$ $r = \frac{0.1765 \cdot 100}{9} \approx 1.96\%$

Conclusion:

• To find the amount taken ($x$), use: $x = \frac{P}{1 + \frac{t \cdot r}{100}}$
• To find the rate of interest per month ($r$), use: $r = \left( \frac{\frac{P}{x} - 1}{t} \right) \cdot 100$

These formulas help in solving for the required variables given the specific conditions and inputs.