P500,000 loan to be repaid quarterly in 5 years. The interest rate applied is 6% convertible quarterly. The quarterly payment is solved as P32,073.56. How much is the outstanding balance after 3 years?
To find the outstanding balance after 3 years, we first need to calculate the total number of quarters in 3 years. Since there are 4 quarters in a year, 3 years would have 3 * 4 = 12 quarters.
Next, we can use the formula for the present value of an ordinary annuity to find the loan amount. The formula is:
Loan Amount = Payment Amount * (1 - (1 + interest rate)^-n) / interest rate
Where:
Payment Amount = P32,073.56 (the quarterly payment)
Interest rate = 6% per quarter, which is 0.06
n = 5 years * 4 quarters per year = 20 quarters
Using these values, we can calculate the loan amount:
Loan Amount = 32073.56 * (1 - (1 + 0.06)^-20) / 0.06
Loan Amount ≈ P419,018.47
Now, to find the outstanding balance after 3 years, we need to calculate the future value of the remaining loan balance. We can use the formula for the future value of an ordinary annuity:
Future Value = Present Value * (1 + interest rate)^n
Where:
Present Value = Loan Amount
Interest rate = 6% per quarter, which is 0.06
n = 12 quarters (3 years)
Using these values, we can calculate the outstanding balance:
Outstanding Balance = 419018.47 * (1 + 0.06)^12
Outstanding Balance ≈ P497,013.47
Therefore, the outstanding balance after 3 years is approximately P497,013.47.