Seasonal Loan Amortization

Question

Hi I can compute a Basic Loan Amortization Schedule, But now I'm trying to Calculate a Seasonal Loan Amortization Schedule . So for example A loan starts at January And Will go on for 3 years, with Monthly Payments. Interest is at 3% Annually and is compounded Annually. During the months of September, October, November, December It'll only accumulate Interest But no payments and principal. Principal is 100000. How Do I calculate Payments and interest.

Answer 1

You can calculate the payments as shown below. But first a basic monthly payment calculation to show the method :-

s = 100000
t = 3
n = 12
i = 0.03

The basic case using the formula here :-

This formula needs the periodic rate, r

r = (1 + i)^(1/n) - 1

monthly payment = (r*s)/(1 - (1 + r)^(-(n*t)))

2906.34

Now the same calculation using a more complicated formula given here :-

In the formula each a(1 + i)^(-k/n) term is a payment. Solving gives the monthly payment ,a, as demonstrated earlier.

By omitting payments for September, October, November & December, (since a for these dates is zero), solving finds the payment amount for the remaining 24 months.

So to repay the loan in 24 equal payments each payment should be 4338.17.

The interest remains 3% annually.

(This method uses EU APR, so you may need to convert your rate first.)

Edit

Taking another go to match the output of the Hema calculator.

Here is the output to be matched :-

First a simple longhand calculation, solved using Mathematica :-

r = 0.03/12;

p[0] = 100000;
p[1] = p[0] - (a - r p[0]);
p[2] = p[1] - (a - r p[1]);
p[3] = p[2] - (a - r p[2]);
p[4] = p[3] - (a - r p[3]);
p[5] = p[4] - (a - r p[4]);
p[6] = p[5] - (a - r p[5]);
p[7] = p[6] - (a - r p[6]);
p[8] = p[7] - (a - r p[7]);

p[13] = p[8] - (a - r p[8]);
p[14] = p[13] - (a - r p[13]);
p[15] = p[14] - (a - r p[14]);
p[16] = p[15] - (a - r p[15]);
p[17] = p[16] - (a - r p[16]);
p[18] = p[17] - (a - r p[17]);
p[19] = p[18] - (a - r p[18]);
p[20] = p[19] - (a - r p[19]);

p[25] = p[20] - (a - r p[20]);
p[26] = p[25] - (a - r p[25]);
p[27] = p[26] - (a - r p[26]);
p[28] = p[27] - (a - r p[27]);
p[29] = p[28] - (a - r p[28]);
p[30] = p[29] - (a - r p[29]);
p[31] = p[30] - (a - r p[30]);
p[32] = p[31] - (a - r p[31]);

sol = Solve[p[32] == 0, a] ;
a = sol[[1, 1, 2]]

4298.12

Which matches the Hema calculation exactly. The seasonal interest charges match too :-

r p[8]

168.326

r p[20]

85.0034

The main payment amount can also be calculated in one step using the loan formula given at the beginning of this answer like so :-

r = 0.03/12
s = 100000
n = 8
t = 3

monthly payment = (r*s)/(1 - (1 + r)^(-(n*t)))

4298.12