Charles S.

asked • 11/02/12

I have a quastion please.

Find the value of annuity of a =$8000, I = 0.010, n =25

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Aisha S. answered • 11/03/12

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You can use the annuity formula:

A=                                            P  (monthly pay out)

                                               —         *  [1-(1+r)-t (number of months per years for the life of the pay out)]

                                                r   (rate or the interest per month)

Because you are getting paid $8,000 monthly for 12 months for 25 years the rate is .01 interest divided by 12 months.  The time exponent is 12 months times the term of your annuity 25 years.

A=                                                  $8,000

                                                      ————    *  [1-(1+.01/12)-(25*12)]

                                                      .01/12                      

The annuity payment you have to pay is $2,122,734.07.  Your total pay off for the next 25 years is $2,400,000.  Multiply your total number of pay off years (25) by the number of months per each year (12) by your monthly pay off ($8000).  25*12*$8,000=$2,400,000

                                                     

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Douglas S.

I'm not quite sure about this.
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11/03/12

Heather L.

Also, Doug, if you look at the link that I provided, you will see the Present Value formulat at the bottom, which is the same as Aisha's but without the multiplication for compounding because it assumes that interest is compounded once per period, as is common practice.

If you don't compound monthly, then PV = 8000*(1 - (1.010)^-25)/0.010 = $176185.25

Unless the person asking the questions wants to clarify further, can we really assume that there are payments being made monthly?  All we know is that there are 25 terms.

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Douglas S. answered • 11/03/12

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Hi Charles! To find the future value (FV) of an annuity, you need to use the "compound interest" formula. The compound interest formula (using the variable names you included above), is FV = a(1 + i)^n. Note: this is assuming interest is compounding only once per year. All that's left is to plug your numbers into the formula, and calculate! Let's do it ! FV = the unknown value a = the original principal amount (the amount you started with). n = the number of years. i = the interest rate (0.010 is 1% per year). So ... FV = a(1 + i)^n FV = 8000(1 + 0.010)^25 Simplify following PEMDAS! (P)arentheses first! FV = 8000(1.010)^25 (E)xponents next! FV = 8000(1.28243199502) Now (M)ultiply. FV = 10259.46 or $10,259.46. The future value of your original $8000 annuity, earning 1% interest per year, compounded once annually for 25 years, is $10,259.46! Good luck, Charles! Doug
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Heather L.

The formula that you have used only works if made one payment is ever made.  An annuity is contracted to make regular "rent" payments each period.  The question doesn't state when the interests compounds, or how long the periods are, and it doesn't usually matter because the interest usually compounds at the end of each period on annuities.  Though, unless someone is very wealthy it's hard to see that they would put more than $8000 in more than once or twice a year. 

The formula for an ordinary annuity is FV(future value) = a*((1+I)^n - 1)/I

Plugging all this in: FV = $8000*(1.010)^25 - 1)/0.010 = $1,025,845.60

However, if the interests compounds more often than once per period this may be be as Aisha stated above.  

http://thismatter.com/money/investments/present-value-future-value-of-annuity.htm

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11/03/12

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