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Tanzania [10]
2 years ago
13

hat semiannual annuity payment is needed to have $500,000 in 15 years if the annuity pays 6.3% interest

Mathematics
1 answer:
KonstantinChe [14]2 years ago
3 0

The required semiannual annuity payment is $10,256.72

What is future value of an annuity?

The future value of an annuity is the accumulated amount in the future that could be achieved by making a fixed periodic savings, it is a semiannual fixed payment that is required in this case.

The future value formula for an ordinary annuity provided below can be used to determine the semiannual payment needed:

FV=PMT*(1+r)^N-1/r

FV=future value=$500,000

PMT=semiannual payment required=unknown

r=semiannual interest rate=6.3%/2=3.15%=0.0315

N=number of semiannual payments in 15 years=15*2=30

$500,000=PMT*(1+0.0315)^30-1/0.0315

$500,000=PMT*(1.0315)^30-1/0.0315

$500,000=PMT*(2.53557796686568000-1)/0.0315

$500,000=PMT*1.53557796686568000/0.0315

PMT=$500,000/1.53557796686568000*0.0315

PMT=$10,256.72

Find out more about future value of an ordinary annuity on:brainly.com/question/14761171

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The cost of 3 notebooks and 4 pencils is $8.50. Determine the cost of one notebook and one pencil
Assoli18 [71]
Call the notebooks x, and the pencils y. 
<span>3x + 4y = $8.50 and 5x + 8y = $14.50 </span>
<span>Then just solve as simultaneous equations: </span>
<span>3x + 4y = $8.50 </span>
<span>5x + 8y = $14.50 </span>

<span>5(3x + 4y = 8.5) </span>
<span>3(5x + 8y = 14.5) </span>

<span>15x + 20y = 42.5 </span>
<span>15x + 24y = 43.5 </span>

<span>Think: DASS (Different Add, Similar Subtract). 15x appears in both equations so subtract one equation from the other. Eassier to subtract (15x + 20y = 42.5) from (15x + 24y = 43.5) </span>

<span>(15x + 24y = 43.5) - (15x + 20y = 42.5) = (4y = 1) which means y = 0.25. </span>

<span>Then substitue into equation : </span>
<span>15x + 20y = 42.5 </span>
<span>15x + 5 + 42.5 </span>
<span>15x = 42.5 - 5 = 37.5 </span>
<span>15x = 37.5 </span>
<span>x = 2.5 </span>

<span>15x + 24y = 43.5 </span>
<span>15(2.5) + 24(0.25) </span>
<span>37.5 + 6 = 43.5 </span>

<span>So x (notebooks) are 2.5 ($2.50) each and y (pencils) are 0.25 ($0.25) each.</span>
6 0
3 years ago
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