Question

In 250 words or words, describe amoratization formula/calculations?

Answer 1

Amoratization:-

The amortization repayment model factors varying amounts of both interest and principal into every installment, though the total amount of each payment is the same. Amortization is paying off an amount owed over time by making planned, incremental payments of principal and interest. To amortize a loan means "to kill it off.

For derivation of amoratization, we will use Net Present Value formula:-

Here C0 = Initial amount of loan / loaned amount

C1 = C2 = ... = Cn = C = per period payment (which is equal through out the loan schedule)

R = Interest rate

N = No. of periods

Now per period payment shall be such that Net present value of all the cash flows becomes zero...

So in above formula

Now the right hand side is a GE term so we will find the sum of n series with below formula:-

Here a = First term

r = Ratio of Second term to first term = 1 / (1+R) (this should be constant all over the series i.e. with third to second, fifth to fourth and so on)

By putting values from NPV formula into above equation we get

After solving further we get

Here per period payment will be

So above is the formula for calculating the per period payment

and this will be constant throughtout the schedule of amoratization.

Now with help of above formula and simple interest formula we can also get principal payment for each period.

Please refer below table in which it is assumed that a $1000 loan has been taken with 8% interest rate and for 3 year payment.

So from above formula our per period payment will be

Now please refer below table for each year principal due, interest amount.

Year	Principal due	Interest	Per period Payment	Principal payment
0	1000	0	0	1000
1	1000	80	388.03	308.03
2	691.97	55.3576	388.03	332.6724
3	359.2976	28.74381	388.03	359.286192

In above table,

- Interest = Principal due * 0.08

- Principal payment = Per period Payment - Interest

- Principal due = Previous year principal due - principal payment

So by using above we can calculate each period principal amount and interest amount.

Thank You!!