Loan Calculation Formulas

1. Fixed Annual Interest Rate:
Monthly installment = (P * r * (1 + r)^n) / ((1 + r)^n - 1)
Whe
P = Principal amount (800,000 in your case)
r = Monthly interest rate (5.9% / 12 = 0.00492)
n = Total number of months (20 years * 12 months = 240)

Monthly installment for fixed annual interest rate loan = 5,327.68

2. Reducing Balance Annual Interest Rate:
Monthly installment = (P * r * (1 + r)^n) / ((1 + r)^n - 1)
Whe
P = Principal amount (800,000 in your case)
r = Monthly interest rate (5.9% / 12 = 0.00492)
n = Total number of months (20 years * 12 months = 240)

However, for reducing balance loans, the outstanding balance changes every month. Therefore, the monthly interest rate will also change. The formula to calculate the monthly interest rate for reducing balance loans is:

Monthly interest rate = Outstanding balance * Monthly interest rate

The monthly installment for the reducing balance annual interest rate loan would be different for each month, depending on the outstanding balance. The calculation for each month would be as follows:

1. Month 1:
   Interest = 800,000 * 0.00492 = 3,936
   Principal = Monthly installment - Interest = 5,327.68 - 3,936 = 1,391.68
   Outstanding balance = Principal = 798,608.32
   
2. Month 2:
   Interest = 798,608.32 * 0.00492 = 3,934.28
   Principal = Monthly installment - Interest = 5,327.68 - 3,934.28 = 1,393.40
   Outstanding balance = Previous outstanding balance - Principal = 798,608.32 - 1,393.40 = 797,214.92
   
   And so on for the remaining months.

Therefore, the monthly installment for the reducing balance annual interest rate loan would vary each month.