I have purchased a machine worth P1,732,173.00. And it needs maintenance every 6 months starting from its purchased date for the first 10 years of its useful life. The maintenance cost is equivalent to the 2% of the total machine cost. How much money should be prepare today to finance the requirement if the interest rate is 0.10 compounded quarterly? with format: GIVEN: REQUIRED: SOLUTION:

## GIVEN:<br />- Machine cost: P1,732,173.00<br />- Maintenance cost: 2% of the total machine cost<br />- Maintenance frequency: every 6 months<br />- Maintenance period: first 10 years of the machine's useful life<br />- Interest rate: 0.10 compounded quarterly<br /><br />## REQUIRED:<br />Amount of money to be prepared today to finance the maintenance requirement<br /><br />## SOLUTION:<br />To calculate the amount of money to be prepared today, we need to find the present value of the maintenance costs over the 10-year period.<br /><br />First, let's calculate the total number of maintenance periods over 10 years. Since maintenance is done every 6 months, there will be 2 maintenance periods per year. Therefore, the total number of maintenance periods is 10 years * 2 = 20 periods.<br /><br />Next, let's calculate the interest rate per period. Since the interest rate is compounded quarterly, we need to divide the annual interest rate by the number of compounding periods per year. In this case, the interest rate per period is 0.10 / 4 = 0.025.<br /><br />Now, we can calculate the present value of the maintenance costs using the formula for the present value of an annuity:<br /><br />PV = PMT * (1 - (1 + r)^(-n)) / r<br /><br />Where:<br />- PV is the present value<br />- PMT is the periodic payment (maintenance cost)<br />- r is the interest rate per period<br />- n is the total number of periods<br /><br />In this case, the periodic payment (maintenance cost) is 2% of the total machine cost, which is 0.02 * P1,732,173.00 = P34,643.46.<br /><br />Plugging in the values into the formula, we get:<br /><br />PV = P34,643.46 * (1 - (1 + 0.025)^(-20)) / 0.025<br /><br />Solving this equation will give us the amount of money that should be prepared today to finance the maintenance requirement.