How to Calculate Housing Loan Installments

Balance Method or Valid Interest

In the so-called “balance method” or “merchant interest”, each installment is first used to redeem principal debt. Installments following principal redemptions are used for the redeeming of accumulated interest.

Example: If a 500,000 TL loan is redeemed in 12 equal installments in the form of monthly payments of 43.860 TL,

Total debt payment: 12 x 43.860 = 526.320 TL

Total interest payment: 526.320 — 500.000 = 26.320 TL

Since the person using the loan makes equal monthly installment payments, the 500,000 TL credit balance is valid only for the first month. When the installment payment of 43.860 TL is made at the end of the first month, the principal balance will decrease to 456.140 TL. The balance will be reduced to 412.280 TL with the payment of the following installment in a month. In this way, installments will continue for 12 months until the debt has expired. Since the total interest payable on the loan at the end of the year is 26.320 TL, this interest will be equal to the use of TL 3.105.240 TL for 1 /12 months. This corresponds to 10.17% with a simple interest,

Interest payment = principal x Interest x Term

26.320 = 3.105.240 x Interest x (1/12)

Interest = (26.320 x 12)/3.105.240 = 0.1017 = 10.17%

Fixed Rate Method

In the “fixed rate method”, each installment payment consists of two parts. The first part is the principal payment, and the second part is the interest payment. The fixed rate method assumes that principal and interest payments are equal proportions. According to this method, if the loan of 500.000 TL with a total interest payment of 26.320 L, which we exemplify above, would have been paid only principal in 12 installments, installments would be 2.194 TL. Therefore, 42.666 TL of the monthly loan installment payment of 43.860 TL is used in principal redemptions and 2194 TL is used for interest payment. The balance of the loan with respect to installment payments will be formed as follows.

Since the total interest payable on the loan at the end of the year is 26,320 TL, this interest will be equal to the 1/12 month use of 3,249.780 TL. This corresponds to 9.71% with a simple interest.

Interest payment = principal x Interest x Term

26.320 = 3.249.780 x Interest x (1/12)

Interest = 26.320 x 12/3.249.780 = 0.0971 = 9.71%

Real estate loans, especially those that are put, usually involve installment payments of equal amounts, at equal intervals of time in a certain term. This type of payment is called “Anuite” The time interval of payments can be monthly, quarterly, six-month or annual. Anuities can also be limited to a certain time, as in the case of 5- or 10-year mortgage loan examples, as in life insurance policy payments, they can be infinite.

Anuite sum = Installment amount x {A, number of periods, period interest}

In anuite calculations, ready-made anuite tables are used, such as in the following example, showing the intersection values of the period number and period interest (PVIFi, n). It is possible to reach these anuite tables in all sources related to finance.

PV = FvN* (PviFi, n)

It is important to determine the present value (PV) of future serial payments in anuits. In fact, the present value of anuity is the sum of the present value of future serial payments (FvN) that make up anuite. Or if you convert the present value of anuite into serial investments in data interest (i) and payment periods (n), you will reach the sum of anuite. Hence,

Anuite present value x (1+ Period interest) a = Anuite sum

Since loan repayments are made in the form of redemption of principal and interest in equal installment payments, the sum of equal installment payments will be higher than the loan amount. Loans amortized in this way offer a more comfortable payment to those who use a loan, since they are spread over the term of the loan. However, although installment payments are determined equally consistently, the weight of principal and interest in installments varies from period to period. Loans put in are loans that are amortized in this way. By studying the depreciation table of loans, you can see how the principal and interest are proportioned within the loan installment.

Example: A mortgage loan with 4% annual interest in the amount of TL 42,000 will be paid in 6-month installments for the next 5 years. What is the installment amount of the loan? ü

Anuite total = 42.000 TL

Period interest = 4%/2 = 2%

Number of periods = 5 x 2 = 10

Installment = Anuite sum x (1/ A, number of periods, period interest)

Installment amount = 42,000 x (1/A, 10, 2%)

= 42,000 x (1/8,9825) = 4.676 TL

42,000 TL credit is redeemed with 6 months payment periods, 10 installments in 5 years, and each installment payment is 4.676 TL. Thus, the total interest payment will be TL 4.760 and the loan will be repaid as 46.760 TL. However, in the following credit amotization table, please note that from the second month, the principal loan balance with installment payments is also decreasing, so the interest rate in installment payment is gradually decreasing.

TL 4.676, the first installment payment, allowed 3.826 TL principal payment after payment of 840 TL, which is 2% interest of the 42.000 TL balance loan. Thus, the principal balance for the second month decreased to 38.164 TL. The second month will decrease to 763 TL as the interest portion is calculated on this balance. This will allow 3.913 TL of the second installment to be used in the principal payment. In this way, we can say that the interest burden will be greater in the initial periods in housing loans, the interest burden will be greater towards the end of the payment period, the interest burden will decrease towards the end of the payment period and a larger part of installment payments will be used for principal redemption. Although this situation is interpreted among the public as the bank first collects interest, in reality it is a result of the fact that the interest payment is calculated on the principal amount of the balance.

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