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3 years ago

15

A rectangle or patio has a length of 12 1/2 feet and an area of 103 1/8 feet. What is the width of the patio?

1 answer:

AfilCa [17]3 years ago

7 0

The width of the patio is 8 7/25 feet ( I hope I got that right )

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Your teacher asked you to represent 3 more than 8 multiplied by a number t as an expression. You wrote 3 + 8t, and your friend w

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3 years ago

When the effective interest rate is 9% per annum, what is the present value of a series of 50 annual payments that start at $100

ser-zykov [4K]

Answer:

$1,109.62

Step-by-step explanation:

Let's first compute the <em>future value FV.</em>

In order to see the rule of formation, let's see the value (in $) for the first few years

<u>End of year 0</u>

1,000

<u>End of year 1(capital + interest + new deposit)</u>

1,000*(1.09)+10

<u>End of year 2 (capital + interest + new deposit)</u>

(1,000*(1.09)+10)*1.09 +10 =

$\bf 1,000*(1.09)^2+10(1+1.09)$

<u>End of year 3 (capital + interest + new deposit)</u>

$\bf (1,000*(1.09)^2+10(1+1.09))(1.09)+10=\\1,000*(1.09)^3+10(1+1.09+1.09^2)$

and we can see that at the end of year 50, the future value is

$\bf FV=1,000*(1.09)^{50}+10(1+1.09+(1.09)^2+...+(1.09)^{49}$

The sum

$\bf 1+1.09+(1.09)^2+...+(1.09)^{49}$

is the <em>sum of a geometric sequence </em>with common ratio 1.09 and is equal to

$\bf \frac{(1.09)^{50}-1}{1.09-1}=815.08356$

and the future value is then

$\bf FV=1,000*(1.09)^{50}+10*815.08356=82,508.35564$

The <em>present value PV</em> is

$\bf PV=\frac{FV}{(1.09)^{50}}=\frac{82508.35564}{74.35572}=1,109.616829\approx \$1,109.62$

rounded to the nearest hundredth.

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3 years ago