Final answer:
The monthly payment for a loan of P250,000 with a 9% interest rate compounded monthly over five years is approximately P5,140.79. This is calculated using the formula for installment payments on an annuity with compound interest.
Step-by-step explanation:
To calculate the monthly payment on a loan of P250,000 with an interest rate of 9% compounded monthly over five years, we can use the formula for the monthly payment (M) which is derived from the amortization formula:
M = P [i(1+i)^n] / [(1+i)^n - 1]
Where:
- P is the principal amount (P250,000)
- i is the monthly interest rate (9%/12 months = 0.0075)
- n is the total number of payments (5 years * 12 months = 60)
Substituting the values, we get:
M = 250,000 [0.0075(1+0.0075)^60] / [(1+0.0075)^60 - 1]
Calculating further:
M = 250,000 [0.0075(1+0.0075)^60] / [(1+0.0075)^60 - 1]
M = 250,000 [0.0075(6.162351)] / [6.162351 - 1]
M = 250,000 [0.04621763] / [5.162351]
M = 11554.4075 / 5.162351
M ≈ P5,140.79
Therefore, the monthly payment for a loan of P250,000 at 9% interest compounded monthly for five years is approximately P5,140.79.