Question

Directions: Show all work, and answer each question that is asked. Define all variables. Explanations should be given in complete sentences. Any graphs should be drawn accurately on graph paper, and axes need to be fully labeled, units accurately scaled, asymptotes drawn in and at least 5 points including x- and y-intercepts clearly labeled. ALL ANSWERS MUST BE JUSTIFIED with work, or a table, or explanations, etc. on how numbers were derived. DO NOT USE LOGARITHMS Phillip wants to have $15,000 in 7 years, so he will place money into a savings account that pays 3.8% interest compounded weekly. How much should Phillip invest now to have $15,000 in 7 years? Write an equation and solve algebraically then verify your answer graphically 1.

Answer 1

  $A=P\left(1+\frac{r}{n}\right)^{nt}$

here

A=15000

r=3.8% = 0.038

n=52 for weekly compound

t=7 years

P=?

15000 = P(1+0. 38)

15000 = P(1+0. 38) 15000 | 1 +

15000P (1 0.00073)04

15000P (1.00073)504 364

15000 = P (1.30461)

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15000 P= (1.30461)

P- 11497.70380

P ะ 11497.7

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phillip needs to invest $ 11497.7

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.

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now equation is

732 0.0381 52 A 11497.7 1+

take years on x-axis and amount after t years on y-axis

to graph the function we need few points

t	732 0.0381 52 A 11497.7 1+
0	$11497.7\left(1+\frac{0.038}{52}\right)^{52*0}\:=11497.7\left(1+\frac{0.038}{52}\right)^{0}={\color{Red} 11497.7}$
1	97.7(1+0.0 )".114977(1+0 0.0385.1 0.038 52 11497.7 | 1 + 11497.7( 1.03872) ). - 11942.8
2	2401407.7(1+0.0 )".11407.7(1+Tas,- 0.038) 104 11497.71 11497.7 1+ 12405.2 - 11497.7(1.07893)-
3	$11497.7\left(1+\frac{0.038}{52}\right)^{52*3}\:=11497.7\left(1+\frac{0.038}{52}\right)^{156}=11497.7( 1.12071)={\color{Red} 12885.5}$
4	$11497.7\left(1+\frac{0.038}{52}\right)^{52*4}\:=11497.7\left(1+\frac{0.038}{52}\right)^{ 208}=11497.7( 1.16410)={\color{Red} 13384.4}$

20000 18000 16000 15000 14000 12000 10000 10 15

as we can see from the graph when t=7 year , amount is 15000

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so our answer is correct