https://file.aiquickdraw.com/mathbot/file/1725511751188fobyivpo.jpg

The problem you uploaded describes a scenario where a company buys a piece of equipment and plans to replace it in the future by setting aside regular payments into a special fund.

Here’s a breakdown of the problem:

1. The company buys equipment for 2 million rupees.
2. The equipment has an expected useful life of 6 years, with no salvage value.
3. The replacement cost is expected to increase by 5% yearly, so they anticipate the equipment's future cost.
4. To replace the equipment, the company sets up a special fund with equal monthly payments at the end of each month for 6 years.
5. The interest rate (cost of capital and earnings) of the fund is 10% per year.

The goal is to compute the **annual payments into the fund**.

To solve this, we will follow these steps:

### Step 1: Calculate the future cost of the equipment after 6 years.
Since the equipment cost is expected to rise by 5% annually, the future value (FV) of the equipment in 6 years is given by the formula:
\[
FV = P \times (1 + r)^n
\]
Where:
- \( P = 2,000,000 \) (initial cost of the equipment),
- \( r = 0.05 \) (5% increase),
- \( n = 6 \) years.

### Step 2: Calculate the monthly payment.
The company plans to make monthly payments into the fund. The formula for monthly payments \( R \) into a fund with regular payments is based on the future value annuity formula:
\[
FV = R \times \frac{(1 + i)^m - 1}{i}
\]
Where:
- \( FV \) is the future value calculated in Step 1,
- \( i \) is the monthly interest rate (annual rate divided by 12),
- \( m = 72 \) (since 6 years = 72 months).

Let me compute both the future cost and the monthly payment.### Results:
1. The future value of the equipment after 6 years (with a 5% annual increase) will be approximately **₹2,680,191.28**.
2. The annual payment that needs to be made into the fund is approximately **₹327,814.34**.

This payment is required to accumulate enough funds to replace the equipment after 6 years, considering the 10% annual interest rate.

---

Would you like further details or have any questions?

Here are 5 related questions for deeper understanding:
1. How does changing the interest rate affect the annual payment required?
2. What happens if the equipment cost increase rate changes from 5% to another value?
3. How would the payment plan differ if the payments were made quarterly instead of monthly?
4. What if the company decided to replace the equipment in 5 years instead of 6 years?
5. Can the company afford to skip any payments without affecting the final fund value?

**Tip:** Regular savings plans benefit from higher interest rates, as compounding interest helps accumulate funds faster.

A company bought a piece of equipment for 2 million Rupees on January 1. The expected useful life is six years, and the salvage value is estimated at zero. The company intends to replace the equipment financially. The average expected price increase is 5% yearly. For this purpose, the company creates a special fund with monthly equal payments at the end of each month during the lifetime. The cost of capital and earnings of the fund is 10% per year. Compute the annual payment into the fund.

This problem involves determining the annual payment into a fund set up to replace a piece of equipment after 6 years. The equipment costs ₹2 million, with a yearly price increase of 5% and a fund interest rate of 10%. Using annuity and future value formulas, find the required annual contribution.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation