184k views
3 votes
A loan of P250,000 is to be canceled by equal monthly payments for five years. If interest is at 9% compounded monthly, how much is the monthly payment?

User Kenorb
by
7.2k points

1 Answer

2 votes

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.

User Mitsuruog
by
7.8k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.