An engineering student wants to purchase a laptop worth P100,000 for academic and engineering projects. The...

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An engineering student wants to purchase a laptop worth P100,000 for academic and engineering projects. The student plans to pay for the laptop through equal monthly payments at an interest rate of 10% per year, compounded monthly, for 1 year.
The first payment will be made at the end of the 4th month, followed by equal monthly payments thereafter.
Determine the required monthly payment and construct the amortization schedule.

SnapAndSolve AI · Accepted Answer

To determine the required monthly payment, we use the formula for the present value of an annuity:

PV = PMT × [(1 - (1 + r)^-n) / r]

Where:

PV is the present value (P100,000).
PMT is the monthly payment.
r is the monthly interest rate (10% per year / 12 months = 0.8333% per month or 0.008333).
n is the number of payments (9 payments, since the first payment is at the end of the 4th month).

Rearranging the formula to solve for PMT gives:

PMT = PV / [(1 - (1 + r)^-n) / r]

Substituting the values:

PMT = 100,000 / [(1 - (1 + 0.008333)^-9) / 0.008333]

Calculating this gives:

PMT ≈ P11,274.57

To construct the amortization schedule, calculate the interest and principal components of each payment, and update the remaining balance after each payment. The schedule will show the breakdown for each of the 9 payments.

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