# Season Loan Amortization with Fixed Payments for low season

From Seasonal Loan Amortization I've learned how to calculate Loan amortization with interest Payments and No payments. I'm wondering how do you calculate it when they only want the borrower to pay a fixed amount during the low seasons.

``````Principal: \$100,000
Interest Rate: 8.5%
Periods: 120
Payment Frequency: Monthly
Disbursal Date: January 1st 2014
Compounding Semi-Anually
``````

For Months 7-12 it'll be a payment of \$500,

Given:

``````Interest Rate: 8.5%
Compounding Semi-Anually
``````

The effective annual rate, `e = (1 + 0.085/2)^2 - 1`

and the monthly rate is, `r = (1 + e)^(1/12) - 1 = 0.00696106`

``````Periods: 120
Payment Frequency: Monthly
``````

So years, `y = 10`

``````Principal: \$100,000
``````

Payments for months 1 to 6 of each year are \$1,934.20

Payments for months 7 to 12 of each year are \$500

Note the calculation above does not reduce to a convenient formula as does the case with equal repayments, i.e.

Dividing top and bottom by `(1 + r)^n` produces the Loan Payment Formula:

Calculation with an interest holiday in the low season

It's not straightforward applying this to the method used by the Hema calculation in the Seasonal Loan Amortization post because the Hema calculator gives an interest holiday in the low season. (That is how their calculation works out to 24 periods over 3 years. For 12 periods there are no payments and neither is any interest charged on the balance, through Sept to Dec).

If fixed payments are to be made in the low season in the present case, with no interest charges on the balance in months 7 to 12, the payments in months 1 to 6 can be worked out like this: