Calculating an Annual Interest Payment 4.0

Many loans are amortized: that is there is both interest and equity paid each payment such that the loan is fully (or partially) paid by the end of the term. However, in such a loan, the interest paid each year changes over the life of the loan. This section calculates the interest paid in a particular year.

Lets consider the previous 200,000 loan on the 260,000 B-T-L in Cambridge. It was a 25 year loan with a fixed interest of 7.10 for 5 years, with payments made monthly. What is the interest paid in year 3 of the loan?

The payment in any year is divided between the equity (e.g. the part that goes toward reducing the loan) and the interest. We also know the total payment each yearin this case, it is 1,426.3425 per month for a total of 17,116.11 per year. Thus, if we knew the change in equity from year 2 to year 3, we could then take that away from the payment and know the interest paid. Remember that year 3 refers to the end of year 2 to the end of year 3.

To calculate the interest paid in any period, follow three steps:

1. Determine the payment

2. Determine the payoff balance at the beginning and end of the period

3. Subtract the change in the payoff balance from the payment- thats interest

Calculator Steps:

1. The payment, calculated by following the steps in part 2, is 1,426.3425 per month

A. Payoff balance at beginning of period

a. Clear and set compound to 12

b. Enter 1,426.3425 Press [PMT]

c. Enter 7.1 Press [I/Y]

d. Enter 276 (23 X 12) Press [N]

e. Press [CPT] then [PV] Display will read -193,753.1797

B. Payoff balance at end of period.

a. Clear and set compound to 12

b. Enter 1,426,3425 Press [PMT]

c. Enter 7.1 Press [I/Y]

d. Enter 264 (22 X 12) Press [N]

e. Press [CPT] then [PV] Display will read -190,282.0321

3. Subtract the payoff balance at the end of the period from the beginning

193,753.1797 190,282.0321= 3,471.1476

Subtract the change in equity from the annual payment

Annual Payment= 12 X 1,426.34= 17,116.11

-3,471.1476

Interest for year 3 13,644.9624

Practice 4

P4.1 What is the interest paid in year 5 of the above loan? Answer