Question 1185511: A 1,200,000 pesos machine was purchased by a company. The said machine has an anticipated economic life of 5 years with a salvage value of 80,000 pesos given that the annual rate of inflation is 7% during the next 5 years. The machine will then be replaced with the same new machine and the company will accumulate the necessary capital by making equal end-of-year deposits in a reserve fund that earns 6% per annum. Determine the amount of actual deposit.
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Here's how to calculate the amount of the annual deposit:
1. **Calculate the future cost of the replacement machine:**
The cost of the machine increases due to inflation. We use the future value formula:
Future Cost = Present Cost * (1 + Inflation Rate)^Economic Life
Future Cost = 1,200,000 * (1 + 0.07)^5
Future Cost = 1,200,000 * 1.40255
Future Cost ≈ 1,683,062.08 pesos
2. **Calculate the amount to be accumulated:**
The company needs to accumulate the future cost of the machine, less the salvage value of the old machine:
Amount to Accumulate = Future Cost - Salvage Value
Amount to Accumulate = 1,683,062.08 - 80,000
Amount to Accumulate ≈ 1,603,062.08 pesos
3. **Calculate the annual deposit:**
We use the future value of an ordinary annuity formula to find the equal end-of-year deposits needed:
FV = A * [(1 + i)^n - 1] / i
Where:
* FV = Future Value (the amount to accumulate) = 1,603,062.08 pesos
* A = Annual Deposit (what we want to find)
* i = Interest rate = 0.06
* n = Number of periods = 5 years
Rearranging the formula to solve for A:
A = FV * i / [(1 + i)^n - 1]
A = 1,603,062.08 * 0.06 / [(1 + 0.06)^5 - 1]
A = 96,183.7248 / [1.3382255776 - 1]
A = 96,183.7248 / 0.3382255776
A ≈ 284,377.44 pesos
**Therefore, the amount of the actual deposit is approximately 284,377.44 pesos.**
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