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1. Find the future value of the following ordinary annuity,

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if payments are made and...
1. Find the future value of the following ordinary annuity, if payments are made and interest is compounded as given.
R=4600;8.73% interest compounded quarterly for 9 years

2. Find the future value of the following annuity due.
$1500 deposited at the beginning of each semiannual period for 11 years at 5.6% compounded semiannually
Submitted: 8 years ago.Category: Math Homework
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Answered in 43 minutes by:
6/23/2010
Math Tutor or Teacher: jimedc,
 replied 8 years ago
jimedc
Category: Math Homework
Satisfied Customers: 524
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1. I assume you mean there are payments of 4600 and the interest per quarter is 8.73% divided by 4 or 2.1825%.

 

The future value after 9 years or 36 periods with payments at the end of the period would be

4600(1 + r +r^2 ...+ r^35) or 4600(r^36 - 1)/(r-1) where r = 1+0.021825 = 1.021825.

 

This gives us 4600 times 53.825928 = 247 752.70 to the nearest hundredths. This is what such a series of payments invested at 8.73% compounded quarterly would be worth in 9 years. This compares to 4600 times 36 = 165 600 which would be the actually amount of money paid out.

 

2. 5.6% compounded twice a year would be 2.6% per period--and 11 years means 22 periods. With deposits made at the beginning of each period we get

 

1500(r + r^2 + ..+r^22) where r = 1 + 0.028 = 1.028

Factoring out an r we get 1500r(1+ r + r^2 +...+ r^21) = 1500r(r^22 - 1)/(r-1).

 

Given r = 1.028 this becomes 1500(1.028)(1.028^22 - 1)/0.028 or

1500 times 1.028 times 29.8535 = $ 46 034.09 where I am only writing the dollar sign at the last step.



Edited by Jim C on 6/23/2010 at 10:28 PM EST
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