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n200080 [17]
3 years ago
8

Traci wants to buys rings that cost 50 dollars each. A jeweler is offering a offering a deal in which you buy 1 ring and get the

second for 25% of and the 3rd for 50% off.The sales tax is 8%. Traci will buy 3 rings. How much money will Traci save using the deal instead of paying full price for all 3 rings?
Mathematics
1 answer:
ddd [48]3 years ago
6 0
1st ring=$50
2nd ring=$37.50
3rd ring=$25
$50+$37.50+$25 =$112.50 total cost before tax
$112.50 X 1.08=$121.5 total cost and tax
3 X $50 X 1.08=$162 total cost without discount deal
$162 - $121.50 =$40.50 savings
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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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