Chit Calculator finding amount taken, finding Rate of Comput intrest case

Chit Fund Calculator

Select Use Case Calculate Amount Taken Calculate Rate of Interest per Month

Chit Amount (P)

Total Period (in months)

Chit Sequence Number

Rate of Interest per Month (%)

Amount Taken (x)

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When dealing with compound interest, the formula changes slightly. Instead of simple interest, compound interest takes into account the compounding effect over the given period.

Compound Interest Formula

For compound interest, the formula is: $A = P \left(1 + \frac{r}{100}\right)^n$

Where:

• $A$ = the future value of the investment/loan, including interest
• $P$ = the principal investment amount (initial deposit or loan amount)
• $r$ = annual interest rate (decimal)
• $n$ = the number of times that interest is compounded per period

In the context of this problem, we will assume monthly compounding and modify our formula accordingly:

$P = x \left(1 + \frac{r}{100}\right)^t$

Given that $t$ is in months and $r$ is the monthly interest rate, this formula will help us calculate the required variables.

Problem 1: Finding Amount Taken (x) with Compound Interest

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: $P = x \left(1 + \frac{r}{100}\right)^t$

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

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

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: $P = x \left(1 + \frac{r}{100}\right)^t$

Solving for $r$: $\frac{P}{x} = \left(1 + \frac{r}{100}\right)^t$ Taking the $t$th root of both sides: $\left(\frac{P}{x}\right)^{\frac{1}{t}} = 1 + \frac{r}{100}$ Solving for $r$: $\frac{r}{100} = \left(\frac{P}{x}\right)^{\frac{1}{t}} - 1$ $r = 100 \left(\left(\frac{P}{x}\right)^{\frac{1}{t}} - 1\right)$

Example Calculations

1. Finding Amount Taken (x) with Compound Interest:

   • 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 $x$: $x = \frac{100,000}{\left(1 + \frac{2}{100}\right)^9}$ $x = \frac{100,000}{(1.02)^9} \approx \frac{100,000}{1.194052} \approx 83,739.06$

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

   • 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 $r$: $\frac{100,000}{85,000} = \left(1 + \frac{r}{100}\right)^9$ $1.1765 = \left(1 + \frac{r}{100}\right)^9$ Taking the 9th root of both sides: $1.1765^{\frac{1}{9}} = 1 + \frac{r}{100}$ $1.018 = 1 + \frac{r}{100}$ $\frac{r}{100} = 1.018 - 1$ $r = 100 \times 0.018 \approx 1.8\%$

Conclusion:

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

These formulas will help in solving for the required variables given the specific conditions and inputs when compound interest is considered.