Some mortgage borrowers have only two things in mind: "How much can I afford?" and "What will my monthly payments be?" They max out their finances on mortgage debt and use an interest-only or negative amortization mortgage to minimize their monthly payments. Then, they rely upon home price appreciation to eclipse the risks associated with a constant or increasing mortgage balance.

In many cases, if these homeowners are fortunate enough to accumulate some equity in their homes, they max out their finances again through a home-equity loan or cash-out refinances and then use the proceeds to make additional purchases, pay down consumer debt, or even make additional investments. Sound risky? It is. In this article, we'll show you how to make sure you have a mortgage you can afford and to build equity by paying it off quickly.

## Making Mortgage Math Add Up

Every mortgage has an amortization schedule. An amortization schedule is a table that lays out each scheduled mortgage payment in a chronological order beginning with the first payment and ending with the final payment. (To read more on amortizations, see *Understanding the Mortgage Payment Structure* and *Make A Risk-Based Mortgage Decision*.)

In the amortization schedule, each payment is broken into an interest payment and a principal payment. Early in the amortization schedule, a large percentage of the total payment is interest, and a small percentage of the total payment is principal. As you pay your mortgage, the amount that is allotted to interest decreases and the amount allotted to principal increases.

The amortization calculation is most easily understood by breaking it into three parts:

**Part 1 - Column 5: Total Monthly Payments**

The calculation of the total monthly payment is shown by the formula below.

$\begin{aligned} &\text{A} = \frac { \text{P}_i }{ 1 - ( 1 + i ) ^ {-n} } \\ &\textbf{where:} \\ &\text{A} = \text{periodic payment amount} \\ &\text{P} = \text{mortgage's remaining principal balance} \\ &i = \text{periodic interest rate} \\ &n = \text{number of remaining scheduled payments} \end{aligned}$

**Part 2 - Column 6:** **Periodic Interest**

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Figure 1

The calculation of the periodic interest charged is calculated as shown below:

**The periodic interest rate (Column 3) x the remaining principal balance (Column 4)**

Note: The interest rate shown in Column 3 is an annual interest rate. It must be divided by 12 (months) to arrive at the periodic interest rate.

**Part 3 - Column 7: Principal Payments**

The calculation of the periodic principal payment is shown by the formula below.

**The total payment (Column 5) – the periodic interest payment (Column 6)**

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Figure 2

Figure 2 shows an amortization schedule for a 30-year 8% fixed-rate mortgage. For the sake of space, only the first five and the last five months are shown.

The amortization schedule demonstrates how paying an additional $300 each month toward the principal balance of the same mortgage shown in Figure 1 will shorten the life of the mortgage to about 21 years and 10 months (262 total months versus 360), and reduce the total amount of interest paid over the life of the mortgage by $209,948.

As you can see, the principal balance of the mortgage decreases by more than the extra $300 you throw at it each month. It saves you more money by cutting down the months of interest charged on the remaining term.

For example, if an extra $300 were paid each month for 24 months at the start of a 30-year mortgage, the extra amount by which the principal balance is reduced is greater than $7,200 (or $300 x 24). The actual amount saved by paying the additional $300 per month by the end of the second year is $7,430.42. You've saved yourself $200 in the first two years of your mortgage - and the benefits only increase as they compound through the life of the mortgage!

This is because when the extra $300 is applied toward the principal balance of the mortgage each month, a greater percentage of the *scheduled* mortgage payment is applied to the principal balance of the mortgage in subsequent months. (Find out more about mortgage payments in our *Mortgage Basics* tutorial.)

## The True Benefits of Making Accelerated Mortgage Payments

The true benefits of making the accelerated payments are measured by calculating what is saved versus what is given up. For example, instead of making an extra $300 per month payment toward the mortgage shown above, the $300 could be used to do something else. This is called a cost-benefit analysis.

Let's say that the consumer with the mortgage shown in the amortization schedules above is trying to decide whether to make the $300 per month accelerated mortgage payments. The consumer is considering three choices as shown below. For each option, we'll calculate the costs versus the benefits, or what can be saved versus what is given up. (For the sake of this example, we're going to assume that leveraging any equity in the home through a home equity loan is not an option. We're also going to ignore the tax deductibility of mortgage interest, which could change the numbers slightly.)

The homeowner's three options include:

- Getting a $14,000 five-year consumer loan at an interest rate of 10% to buy a boat.
- Paying off a $12,000 credit card debt that carries a 15% annual rate (compounded daily).
- Investing in the stock market.

*Option 1: Buying a boat*

The decision to buy a boat is both a matter of pleasure and economics. A boat—much like many other consumer "toys" - is a depreciating asset. Adding household debt to purchase an illiquid, depreciating asset adds risk to the household balance sheet. This consumer has to weigh the utility (pleasure) gained from owning a boat versus the true economics of the decision.

We can calculate that a $14,000 loan for the boat at an interest rate of 10% and a five-year term will have monthly payments of $297.46.

*Cost-Benefit Breakdown*

If the homeowner had made $300 accelerated payment for the first five years of the mortgage rather than buying a boat, this would have shortened the life of the mortgage by 47 months, saving $2,935.06 for 47 months, 313 months in the future. Using a 3% discount rate this has a present value of $59,501. Additionally, if the accelerated mortgage payments are made, the principal balance of the mortgage will be reduced by an additional $21,599 by the end of the five-year period. This early retirement of debt reduces risk on the household balance sheet. (To learn more about compounding's effects on your loans, see *Understanding The Time Value Of Money*.)

By deciding to purchase the boat, the consumer spends $297.46 per month for five years to own a $14,000 boat. The $297 per month for 60 months equals out to a present value of $16,554.

By putting the $300 on the mortgage, this consumer would save $59,501 over the course of the mortgage. Buying the boat would mean spending $16,554 to pay for a $14,000 boat that is likely to have a depreciating resale value.

Therefore, the consumer must ask himself if the pleasure of owning the boat is worth the large divide in the economics.

*Option 2: Paying off a $12,000 credit card debt*

The daily compounding of credit card interest makes this calculation complex. Credit card interest is compounded daily, but the consumer is not likely to make daily payments. However, the calculation of an amortization schedule says that if the consumer pays about $300 per month for five years, that person can eliminate the credit card debt.

As in the first example, making accelerated payments on the mortgage of $300 each month for the first five years will leave the homeowner with a present value of future payment savings of $59,501.

By paying $300 per month for five years to eliminate the credit card debt, the consumer can eliminate $12,000 in credit card debt with a 15% annual interest rate.

We know that if the consumer makes accelerated mortgage payments, the credit card debt will continue to accrue interest and the outstanding balance will increase at an increasing rate. If we compound $12,000 daily at an annual rate of 15% for 60 months we get $25,400. If we assume that after making five years of accelerated mortgage payments, the consumer could then start to pay down the credit card debt by $300 per month, it would take more than 50 years at $300 per month to pay off the credit card debt at that point. In this case, paying down the credit card debt first is the most economical choice.

*Option 3: Invest in the stock market*

We've already shown that the consumer will save a present value of $59,501 by making accelerated mortgage payments of $300 for the first five years of the mortgage. Before we compare the accelerated mortgage payment savings to the returns that might be made in the stock market over the same time period, we must point out that making any assumptions about stock market returns is extremely risky. Stock market returns are volatile. The historical average annual returns of the S&P 500 Index is about 11%, but some years it is up, and some years it is down.

Putting the $300 toward the mortgage means a present value of $59,501 of future mortgage payments and a reduction of $21,599 in the principal balance of the mortgage over the first five years of the mortgage. This reduces the risks associated with debt.

If the consumer decides to invest the $300 monthly over a five-year period in the stock market - assuming an average annual return of 11% - this will yield a total portfolio value of $23,855 which has a present value of $20,536 (discounted at 3%), which is far less than the present value $59,501 realized by making accelerated mortgage payments.

However, if we assume the $23,855 will continue to earn an annual return of 11% beyond month 60 - until month 313, the point at which the mortgage payment would be eliminated - the total value of the portfolio at that point would be $239,989. This is greater than the present value of future mortgage payment savings at that future time, which would be $129,998.

We could conclude then that investing in the stock market over the long term might make more economical sense - but this would only be a given in a perfect world.

## The Bottom Line

Homeowners need to understand that bigger mortgage is compared to the value of the home, the larger the risk they have taken on. They must also be aware that home price appreciation should not be relied on to eclipse the risks of mortgage debt. Furthermore, they need to understand that paying down mortgage debt reduces risk and can be to their economic advantage.

One of the key aspects of making accelerated mortgage payments is that each dollar reduction in the outstanding principal balance of a mortgage reduces the amount of interest paid as part of future scheduled payments, and increases the amount of principal paid as part of those same payments. Therefore, a simple calculation that sums up the amount of interest saved over a period that ends before the loan is paid off does not accurately capture the entire benefit of making accelerated mortgage payments. A present value calculation of the future payment savings is a more accurate analysis. Additionally, every dollar of principal that is paid down early reduces risk on the household balance sheet.

Still interested in refinancing your mortgage? Then check out *The True Economics Of Refinancing A Mortgage* and *American Dream Or Mortgage Nightmare?*