The economics of finance can be used to analyze some common personal financial issues. Most of these issues will not affect you until you are older, at which point it will help to be able to remember the economic perspective.

Compound Interest

Suppose that you are 30 years old, with a family income of $50,000 a year. If you save $3000 a year, how much will you have after 35 years? The principal alone, without earning interest, will be 35 times $3000, or just $105,000. However, if you invest the money and earn a real annual return of 4 percent, at the end of 35 years you will have $221,000. The difference between $221,000 and $105,000 is the power of compound interest.

Below is a table that shows part of this calculation

In the real world, inflation tends to distort this sort of calculation. Because of inflation, you might be able to earn a return of 7 percent, ending up with a balance of over $400,000. Moreover, if inflation is, say, 3 percent per year, then you should be able to save more than $3000 a year in later years. In fact, your savings should go up by 3 percent per year, which will further increase your final balance. However, if inflation is 3 percent per year, that means that the cost of living after 35 years will be almost triple what it is today. Overall, a world in which the nominal interest rate is 7 percent and inflation is 3 percent is like one in which the nominal interest rate is 4 percent and inflation is zero.

The point to appreciate about compound interest is that over a long period of time a relatively small annual rate of savings can add up. On the other hand, living beyond your means and going into debt means that compound interest works against you. Adding a little more debt each year can lead you into a very deep hole. The compounding effect is even stronger, because interest rates for consumers tend to be high (over 10 percent on many credit cards). If you do not pay your full credit card balance every month, you end up fighting a very strong current of compound interest flowing against you.

Our general formula for the profitability of buying a home is based on a comparison of the purchase price to the rent on an equivalent home. The formula is

profitability = rental rate + appreciation - interest rate

For example, if a house costs $150,000 and it could be rented for $6,000 a year, then the rental rate is $6,000/$150,000 = .04 or 4 percent. If it appreciates at a rate of 4 percent per year and the interest rate is 7 percent, then the profitability is 4+4-7=1 percent, which means that it is profitable to buy the house rather than rent.

A major complicating factor with buying a house is that it costs a lot to buy and sell. Real estate sales commissions are around 6 percent. There are also a number of fees charged by lenders, title insurance companies, and other service providers. Finally, the local government often collects transfer taxes and fees for recording the transaction.

The costs of buying and selling a home affect the home-buying decision in many ways. Basically, the sooner you have to sell a house, the less likely it is to be profitable to buy rather than to rent.

If you are likely to be moving soon because of a job change or a change in family status, it can be unwise to buy a house. When you are starting a family, it may be better to buy a house with an extra bedroom now, rather than buy one house this year and another in two years when you have more children.

Because profitability depends so much on home price appreciation, one does not want to buy a house when prices are too high. In an efficient market, there should be no way of telling when prices are out of line. However, house prices sometimes seem to reach irrational levels for short periods of time in specific markets. A sign that prices are too high is when the ratio of annual rent to purchase price is unusually low, say less than 2 percent.

The riskiest properties to own are condominiums. Condos tend to be the shock absorbers of the housing market. When demand is high, condo prices soar. When demand falls off, condo prices drop the most.

Most young people do not have enough cash to buy a home. Therefore, you typically have to borrow most of the money to buy a house. The money that you borrow is called a mortgage loan. If you default on a mortgage loan, the lender can take possession of your house. We say that the house is collateral for the mortgage loan. The collateral reduces the lender's risk, so that a mortgage loan costs you less than any other loan that you might obtain.

A typical mortgage loan has a 30-year term, with payments made monthly. The monthly payment is designed to gradually reduce the mortgage balance to zero, just as an annuity payment is designed to gradually exhaust savings. In fact, the formula for calculating a mortgage payment is pretty much the same as the formula for an annuity. The main difference is that the mortgage payment is monthly, so that the interest rate has to be converted to a monthly rate.

Most mortgages are paid off before the 30 year term expires.

• Often, people move and sell their homes, at which point the proceeds from the sale are used to pay the mortgage.
• Sometimes, people refinance their mortgages. If you took out a mortgage loan at 8 percent, and rates happen to drop to 6.5 percent, you will take out a new loan at 6.5 percent to pay off the old loan. Even if rates do not fall, some people refinance in order to take out a larger loan.
• As a family's financial position improves, they find it advantageous to pay off the mortgage loan early

The reason that the thirty-year term is popular is that by stretching out the payments over that period the monthly payments are kept low. However, if you are likely to pay off a mortgage loan in ten years or less, it makes sense to take an adjustable-rate mortgage, where the interest rate can change after 3 years or 5 years. These loans carry lower interest rates than the standard thirty-year fixed rate, but the rate can increase. If you were keeping the loan for ten years or more, the rate increase could be a big issue. However, few people keep their mortgage loans that long.

When you have a mortgage loan on your residence, you can deduct the interest expense from your income. You will hear it said that a mortgage loan is a great tax deduction, and some financial advice gurus even recommend taking out the largest mortgage loan that you can. This is flawed advice, for several reasons.

1. The deductibility of home mortgage interest does not mean that taking out a mortgage loan puts money in your pocket. At best, it reduces the cost of the loan. If your mortgage rate is 7 percent, then on an after-tax basis it might be closer to 5 percent.

2. The tax deduction has many limitations and restrictions. For many people, a mortgage ends up making only a small difference in tax liability.

3. If you take out a larger mortgage than you need, then that gives you money to invest. When you invest that money, you earn taxable income. The taxes on that income tend to cancel out the tax savings from the larger mortgage.

Income taxes do affect personal financial decisions. Other things equal, an investment with tax-exempt income is better than an investment where the income may be taxed. When the income is tax exempt, your savings accumulate more effectively.

The best investment vehicles go even further to save on taxes, because the the money you put into the accounts is tax deductible. If you earn $50,000 and put $2000 into an Individual Retirement Account (IRA), you can deduct the $2,000 from your taxable income as well as accumulate investment earnings tax-free until you retire. Thus, it pays to put money in an IRA.

Similarly, there are employer-sponsored retirement savings plans, called 401(K) plans, because the provision in the tax code is called 401(K). Like IRA's, they allow you to take an income tax deduction for your savings. In addition, many companies have matching programs, where they will kick in additional money in proportion to what you save.

There is almost no valid reason not to take maximum advantage of 401(k) plans and IRA's. Because of the tax advantages, these are the best savings vehicles.

People who want to get the best returns over a long period should put some of their investment portfolio in the stock market. Your stock market portfolio should be in mutual funds that replicate the performance of a major stock index. This approach is known as indexing.

Inside a tax-exempt account, such as an IRA, regular mutual funds, called index funds, provide excellent diversification at low cost. However, regular mutual funds are required to distribute income each year, which has tax consequences. A new instrument, known as exchange-trade mutual funds, allows you to defer taxes until you sell your shares in the funds. An exchange-traded index fund is the best investment vehicle when you are putting savings into a taxable account.