## Annuities

Annuities are one of the hardest areas of high school finance.  An annuity is a series of equal payments that are made at regular intervals.  The interest in annuities is always compound interest.

Without going into the complicated explanations of how the annuity formula is calculated, here it is:

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The Sni is called the annuity factor, for reasons that will become clear in the following example:

 Suppose I make regular payments of \$10.00 every month for 10 years at a compound yearly interest rate of 6% with monthly rests.  How much is my annuity worth after the 10 years? Solution ‘i’ is the interest rate, which is 0.06/12. We divide by 12 because we are making payments every month and using monthly rests – we want the interest rate per month. ‘n’ is the number of payments, which is 10 ´ 12. 10 years ´ 12 months / year = 120.                                                  Now we know the annuity factor.  To work out how much my annuity is worth you simply multiply the regular amount I am investing by the annuity factor:

### Present values of annuities

When people take out a loan from a bank, they must make regular repayments to the bank until they have paid back the loan.  The big upfront amount of money they borrow is called the present value of an annuity.

The formula for this is:

 Calculate how much a person can borrow upfront who wants to pay back \$5000 a year for 10 years at 13% compound interest. Solution Once again, to find out the actual amount that can be borrowed upfront, we multiply the ani by the amount we want to pay back regularly:                                            Notice how this amount is a lot smaller than how much the person would pay back in total over the 10 year period.  This is because the money they borrow up-front could have earned interest if not tied up – they have to pay back extra on top of the upfront amount to compensate the bank for this.