| In the first two parts of this series we discussed how | | | | year mortgage for $100,000 at 6% interest. The way |
| compound interest is computed and the effects of | | | | the bank figures the compounding on mortgages is by |
| various compounding on your net return. Here we | | | | using the monthly nominal rate. Thus at 6%, the nominal |
| discuss how that dreaded of all dreaded payments is | | | | rate is 6%/12 or 0.005. The way we obtain the monthly |
| calculated. What is it?--yes, you got it, that death | | | | payment is by using the formula that states that the |
| pledge of a debt--the mortgage. You'll want to read | | | | monthly payment P times the annuity factor (which we |
| this. | | | | will call an) is equal to the amount borrowed A. Using |
| If you don't already know, mortgage derives from two | | | | 6% and $100,000, this formula translates to P*an = A, |
| French words which mean "death pledge." When you | | | | or P*an = $100,000. |
| consider all the foreclosures that are occurring right | | | | Solving for P, we have P = A/an. All we need to know |
| now after the sub-prime bust, the etymology of the | | | | now is what an is equal to. To find an, we introduce |
| word rings pretty true to life. In this article, we are going | | | | another factor, called the discount factor, and we |
| to discuss the way to calculate your mortgage | | | | denote this by v. V is equal to the reciprocal of one |
| payment based on the specified term and interest | | | | plus the nominal interest rate. Mathematically v = 1/(1+i), |
| rate. You need to understand compound interest and | | | | where i = .005. The annuity factor an is expressed as |
| nominal rates of interest, so if you have not mastered | | | | follows: an = (1 - v^n)/i, where n is the number of |
| these two topics from my articles "The Mathematics | | | | months. |
| of Finance" Parts I & II, go and read those before | | | | Let's take our example of a $100,000 thirty year |
| you try to tackle this one. | | | | mortgage at 6% and calculate our payment P. Note |
| A mortgage is actually a form of an annuity: a | | | | that 30 years is equal to 30*12 or 360 months. V = 1/(1 |
| contract in which one party, in exchange for a lump | | | | + i) or 1/1.005. Thus v is equal to 0.99502, to four |
| sum of money, promises to make a stream of | | | | decimal places. We can now find our annuity factor an. |
| payments over a certain period of time. When a bank | | | | Thus an = (1 - v^n)/i, or (1 - .99502^360)/.005. When |
| gives you a mortgage, the bank is giving you a sum of | | | | we enter this into our calculator we get an = 166.85. |
| money with which to purchase your home, in return for | | | | We can now calculate P as P = $100,000/166.85, or P |
| your series of payments, which are generally paid | | | | = $599.35. |
| every month over a period of thirty years. With the | | | | Yes, that's all there is to calculating that dreaded of all |
| knowledge from the first two articles, you can | | | | dreaded monthly payments. Just remember. This |
| calculate this payment quite easily. | | | | death pledge is not a death pledge unless you make it |
| Let's assume that "Frequent Compounding Bank USA," | | | | one. Don't. |
| your friendly local lending institution, grants you a thirty | | | | See more at my cool math site Problem of the Week. |