What is Mortgage Formula?
The formula for mortgage basically revolves around the fixed monthly payment and the amount of outstanding loan.
The fixed monthly mortgage repayment calculation is based on the annuity formulaAnnuity FormulaAn annuity is the series of periodic payments to be received at the beginning of each period or the end of it. An annuity is based on the PV of an annuity due, effective interest rate and time period. Annuity = r * PVA Ordinary/[1 – (1 + r)-n]read more, and it is mathematically represented as,
where P = Outstanding loan amount, r = Effective monthly interest rate, n = Total number of periods / months
On the other hand, the outstanding loan balance after payment m months is derived by using the below formula,
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For eg:
Source: Mortgage Formula (wallstreetmojo.com)
Explanation
The formula for fixed monthly mortgage repayment calculation and outstanding loan balance can be derived by using the following steps:
- Identify the sanctioned loan amount, which is denoted by P.
- Now figure out the rate of interest being charged annually and then divide the rate of interest by 12 to get the effective interest rate, which is denoted by r.
- Now determine the tenure of the loan amount in terms of a number of periods/months and is denoted by n.
- On the basis of the available information, the amount of fixed monthly payment can be computed as above.
- The fixed monthly payment comprises of interest and a principal component. Therefore, the outstanding loan amount is derived by adding the interest accruedInterest AccruedAccrued Interest is the unsettled interest amount which is either earned by the company or which is payable by the company within the same accounting period.read more form months and deducting fixed monthly payments from the loan principal, and it is represented as above.
Examples
Let’s see some simple to advanced examples of fixed monthly mortgage payment calculation.
Example #1
Let us take the simple example of a loan for setting up a technology-based company and the loan is valued at $1,000,000. Now the charges annual interest rate of 12% and the loan has to be repaid over a period of 10 years. Using the above-mentioned mortgage formula calculate the fixed monthly payment.
where,
No. of periods, n = 10 * 12 months = 120 months
Effective monthly interest rate, r = 12% / 12 = 1%
Now, the calculation of fixed monthly payment is as follows,
- Fixed Monthly Payment = P * r * (1 + r)n / [(1 + r)n – 1]
- = $1,000,000 * 1% * (1 + 1%)120 / [(1 + 1%)120 – 1]
Fixed Monthly Payment will be –
- Fixed Monthly Payment= $14,347.09 ~ $14,347
Therefore, the fixed monthly payment is $14,347.
Example #2
Let us assume that there is a company which has $1,000 of loan outstanding which has to be repaid over the next 2 years. The EMI will be computed at an interest rate of 12%. Now based on the available information calculate
- Loan outstanding at the end of 12 months
- Principal Repayment in the 18th month
Given,
Loan principal, P = $1,000
No. of periods, n = 2 * 12 months = 24 months
Effective interest rateEffective Interest RateEffective Interest Rate, also called Annual Equivalent Rate, is the actual rate of interest that a person pays or earns on a financial instrument by considering the compounding interest over a given period.read more, r = 12% / 12 = 1%
#1 – Loan Outstanding after 12 Months
The calculation of loan outstanding after 12 months will be as follows-
- = P * [(1 + r)n – (1 + r)m] / [(1 + r)n – 1]
- = $1,000 * [(1 + 1%)24 – (1 + 1%)12] / [(1 + 1%)24 – 1]
Outstanding Loan after 12 Months will be-
- Outstanding loan = $529.82
#2 – Principal Repayment in the 18th Month
The principal repayment in the 18th month can be computed by deducting the outstanding loan balance after 18 months from that of 17 months. Now,
Loan Outstanding after 17 Months
- Loan outstanding after 17 months = P * [(1 + r)n – (1 + r)m] / [(1 + r)n – 1]
- = $1,000 * [(1 + 1%)24 – (1 + 1%)17] / [(1 + 1%)24 – 1]
- = $316.72
Loan Outstanding after 18 Months
- Loan outstanding after 18 months = P * [(1 + r)n – (1 + r)m] / [(1 + r)n – 1]
- = $1,000 * [(1 + 1%)24 – (1 + 1%)18] / [(1 + 1%)24 – 1]
- = $272.81
Therefore, the principal repayment in the 18th month will be
- Principal Repayment in 18th Month= $43.91
Relevance and Uses
It is of great importance for a business to understand the concept of a mortgage. The Mortgage Equation can be used to design a loan amortization scheduleA Loan Amortization ScheduleLoan amortization schedule refers to the schedule of repayment of the loan. Every installment comprises of principal amount and interest component till the end of the loan term or up to which full amount of loan is paid off.read more, which shows in detail how much is being paid in interest instead of focusing just on the fixed monthly payment. Borrowers can make decisions based on the interest costs, which is a better way to measure the real cost of the loan. As such, a borrower can also decide, based on the interest savings that which loan to choose when different lenders offer different terms.
Mortgage Calculation (with Excel Template)
Now let us take the case mentioned in example 2 to illustrate the concept of mortgage calculation in the excel template. The table gives a snapshot of the amortization schedule for a mortgage.
Recommended Articles
This has been a guide to Mortgage Formula. Here we discuss how to calculate Monthly Mortgage Repayment and outstanding Loan Balance with the practical examples and downloadable excel sheet. You can learn more about accounting from the following articles –
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