We are given that a man borrowed ₹50,000 at a monthly interest rate of 4%. After paying ₹84,000, he cleared the debt. We need to determine the time it took for him to become free from the debt.

Formula for Simple Interest

The formula for simple interest is:

$A = P(1 + rt)$

Where:

• $A$ is the total amount paid (₹84,000),
• $P$ is the principal (₹50,000),
• $r$ is the rate of interest per month (4% or 0.04),
• $t$ is the time in months.

Substituting the Given Values

Substituting the values into the formula:

$84,000 = 50,000(1 + 0.04t)$

Now, let's solve for $t$.

1. First, divide both sides by 50,000: $\frac{84,000}{50,000} = 1 + 0.04t$ $1.68 = 1 + 0.04t$

2. Subtract 1 from both sides: $0.68 = 0.04t$

3. Solve for $t$: $t = \frac{0.68}{0.04}$ $t = 17 \text{ months}$

Answer:

It took 17 months for the man to become free from the debt.

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Would you like further details on how this interest calculation works, or do you have any other questions?

Related Questions:

1. How would the amount paid change if the interest rate were higher or lower?
2. What would the total payment be if the interest rate were 5% instead of 4%?
3. How would the formula change if compound interest were used instead of simple interest?
4. If the man paid ₹90,000, how long would it have taken him to clear the debt?
5. What is the total interest paid by the man after 17 months?

Tip:

When dealing with simple interest, the total amount paid increases linearly with time.