Maintenance cost of an equipment is P20,000 for 2 years, P40,000 at the end of 4 years, and P80,000 at the end of 8 years. Compute the semi-annual amount that will be set aside for this equipment. Money worth 10% compounded annually.
My answer is P152,166.38. Is it correct? If not, can anyone give me the final answer or the steps on how to correctly do it?
I think my answer was wrong. It should be P7,425. Am I right?
Convert Annually to Semi-annually
i(annually)=i(semi-annually)
(1+0.10)^1=(1+X)^2
X=0.0488
P=A( (1-(1+x)^(-8(2)) )/x ) *note: times 2 at the exponent because of semi-annually
P=(20000/(1+x)^(2)(2)) + (40000/(1+x)^(4)(2)) + (80000/(1+x)^(8)(2))
P=81170.05
P=A( (1-(1+x)^(-8(2)) )/x )
81170.05 = A( (1-(1+x)^(-8(2)) )/x )
A=7426.19
Solution pls
Hi! Can you show the solution to this problem? Thank you!
Well, I must say, calculating maintenance costs can be quite a circus act! Let me help you juggle those numbers and figure out the correct answer.
To find the semi-annual amount that should be set aside, we'll need to calculate the present value of the maintenance costs using the formula:
PV = FV / (1 + r/n)^(n*t)
Where:
PV = Present Value (the amount to be set aside)
FV = Future Value (maintenance cost)
r = Interest rate (10%)
n = Number of compounding periods per year (2, for semi-annual)
t = Number of years
Let's begin by calculating the present value for each maintenance cost:
For the P20,000 maintenance cost over 2 years:
PV1 = 20,000 / (1 + 0.10/2)^(2*2)
For the P40,000 maintenance cost at the end of 4 years:
PV2 = 40,000 / (1 + 0.10/2)^(2*4)
For the P80,000 maintenance cost at the end of 8 years:
PV3 = 80,000 / (1 + 0.10/2)^(2*8)
Now, let's add up these present values to get the total amount to be set aside:
Total PV = PV1 + PV2 + PV3
Once you've computed that total, you can compare it to P152,166.38 to see if they match. Remember, it's always good to double-check your calculations, just like a clown double-checks their funny nose!
To correctly compute the semi-annual amount that should be set aside for this equipment, we need to break it down into three periods: 2 years, 4 years, and 8 years.
First, let's calculate the present value of the maintenance costs at the end of each period using the formula for compound interest:
PV = FV / (1 + r/n)^(n*t)
Where:
PV - Present Value
FV - Future Value
r - Annual interest rate (as a decimal)
n - Number of compounding periods per year
t - Number of years
For the first 2-year period:
PV1 = 20,000 / (1 + 0.10/2)^(2*2) = 15,790.12
For the 4-year period:
PV2 = 40,000 / (1 + 0.10/2)^(2*4) = 28,566.20
For the 8-year period:
PV3 = 80,000 / (1 + 0.10/2)^(2*8) = 58,128.07
Now, let's sum up the present values to get the total amount that needs to be set aside for the equipment:
Total PV = PV1 + PV2 + PV3 = 15,790.12 + 28,566.20 + 58,128.07 = 102,484.39
Since you want to compute the semi-annual amount, we need to divide the total present value by the number of semi-annual periods (16 semi-annual periods in 8 years). So:
Semi-annual amount = Total PV / Number of semi-annual periods
= 102,484.39 / 16
= 6,405.27
Therefore, the correct semi-annual amount that should be set aside for this equipment is P6,405.27.
Your answer of P152,166.38 is not correct. It appears to be the result of a different calculation or formula.