Thursday, April 5, 2012

How much interest are you paying?

Personal financial literacy is the first step towards developing true financial security and realizing a dream of quitting a job or having a comfortable retirement. I received an MBA in accounting and now I use my knowledge to help others. People and businesses have a lot of difficulty managing cash flow. Most people don't have visibility into the interest that they are paying. Even though they enacted a law that requires financial institutions to disclose more about interest on credit cards, most consumers don't have a full grasp of the true magnitude of interest, especially on longer term loans like mortgages and some car loans.

The only two forms of robbery that are worse than interest on loans are armed robbery and rent payments. In the former, you are losing something you have and get nothing in return. In the latter, you are basically throwing cash away every month.

Smart financial people never pay more interest than they have to, and they tend to engage in good financial habits like keeping balances low and paying off loans well before their due date. Why? It's how interest works. In most cases, you are charged interest on the unpaid portion of the principal (the amount that you originally borrowed). Each month a portion of your minimum payment goes towards interest and a portion goes towards principal. What no one ever tells you is how much goes each way. Creditors don't want you to know, because if the average American (or anyone in any other country) understood this there would be a very violent revolution against both the creditors (banks, credit unions, mortgage companies, etc) and the government (for letting it happen).

You typically have to pursue a finance or accounting degree in college to learn how to calculate interest on a loan.  I received an MBA specializing in accounting and dealt extensively with loan calculations, and I'm mortified on a daily basis at how much people pay in interest on a 4% home loan (typically over 30 years) or a 6% student loan (typically over 10 years) . Auto loans are also very expensive (typically 5-10 years to pay off). What about "no interest" loans? This is the worst kind of loan because the interest is included in the principal, so there is no way to save money by paying it off early.

The idea behind most loans is that the interest accrues at specific intervals (typically daily, monthly, quarterly, or annually) and is a function of the interest rate and the unpaid principal amount. Most loan disclosure documents give the interest rate in annual terms, so when you receive a 4% mortgage, you will pay roughly 4% of the principal in interest payments over the course of a year, and these interest payments will be calculated (compounded) according to the loan agreement. To initially calculate a loan payment, you need access to a present value calculator to avoid doing a lengthy manual calculation. Every present value calculator has 3 main inputs and an output consisting of the following:
  • PV -  Present Value (the amount you are borrowing)
  • INT - Interest Rate
  • N - Number of Periods to compound interest rate
  • FV - Future Value (Value at the end of the period)
  • PMT - The payment paid or received
By convention, PV and FV are positive if you are receiving cash and are negative if you are giving cash. If you have any 3 of these, you can calculate the 4th with a present value calculator. Back in college, it would have been normal to use a TI BAII+ or an HP 12C, but with any computer running Microsoft Excel or Calc, the functions of a financial calculator are built in. I will build the demonstration spreadsheet with Microsoft Excel.

I typically need to answer the question of "If I buy this house, how much will my mortgage payment be?" In this case, we have to determine a payment given a present value, interest rate, and future value (which is 0).

To calculate a payment, we use the PMT(I,N,PV,FV) function. Most mortgages are compounded monthly, so we would need to divide the annual rate by 12. For a 30 year mortgage, the number of periods is 360, for a 15 year mortgage, the number of periods is 180. A couple of examples follow:

30 year mortgage, compounded monthly, interest rate of 6% annually and borrowing an amount of 200,000:

=pmt(.06/12,360,200000,0) = -$1199.10

15 year mortgage borrowing $500,000 at 7%

=pmt(.07/12,180,500000,0) = -$4494.14

Simple enough, now how do we determine the total amount of interest paid? Inititally, almost the entire loan payment is interest, and over time the balance shifts and the loan payment becomes more principal than interest. The below example shows how a $100,000 loan at 5% breaks down over the lifetime of the loan.

In order to calculate this, we take the values that we specified above for INT, PV, FV, N, and PMT and build a loan amortization schedule. This example will show the first few periods of a $100,000 loan at 5%.

Period Beginning Amount [BA] Payment [PMT] Interest Payment [IP]
Beginning Amount * INT
Principal Payment [PP]
PMT - Interest
Remaining Principal
1 100,000 536.82 416.67 120.15 99,879.85
2 99,879.85 536.82 416.17 120.66 99,759.19
3 99,759.19 536.82 415.66 121.16 99,638.03
... ... ... ... ... ...

Carrying this out to 360 periods, the remaining principal goes to zero and the loan is paid off. To determine the total interest paid on the loan, sum the interest payments column. For the example above, the interest paid on $100,000 at 5% over 30 years is 93,255.78, or almost 94% of the original amount borrowed over the life of the loan. What happens if we pay more than the minimum? Lets take the previous example, but pay $1,000/month instead of the minimum (536.82).

Period Beginning Amount [BA] Payment [PMT] Interest Payment [IP]
Beginning Amount * INT
Principal Payment [PP]
PMT - Interest
Remaining Principal
1 100,000 1000 416.67 583.33 99,416.67
2 99,416.67 1000 414.27 585.76 98,830.90
3 98,830.90 1000 411.80 588.20 98,242.7
... ... ... ... ... ...

In this case, the loan is paid off in 130 periods (just under 11 years) with a total interest amount of $29,628.96. That is a savings of $63,626.82 in interest. That's more than 63,000 that could be put elsewhere, such as paying the loan off even more quickly, investing in passive income sources, and saving additional money for retirement.

If you follow my personal bookkeeping example, you would make similar entries each period for the loan above (this is an example for period 1):

Mortgage                   $583.33 
Mortgage Interest Expense  $416.67
    Cash                            $1000  

The mortgage on the balance sheet reduces by the principal payment and cash decreases by $1,000 to cover the interest and principal payment. The mortgage interest is expensed on the income statement for the period as a cost of borrowing the money for the mortgage.

The moral of the story is to pay off loans as quickly as possible, because you'll pay a ton in interest if you don't. One of the less commonly known points of wisdom is that you have no business putting money into a savings/investment account that has a lower percentage return than the interest rate on your highest loan.

See Also
Retirement in the 21st Century

1 comment:

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