Question 1133089
<font color="black" face="times" size="3">Part (a)


We'll use the compound interest formula shown below


A = P*(1+r/n)^(n*t)


The variables are
A = final amount
P = initial amount (aka deposit)
r = annual interest rate in decimal form
n = number of times money is compounded per year
t = number of years


In this case, we have,
A = 10000 is the final amount we want to have
P = unknown initial amount or deposit (what we want to solve for)
r = 0.055 is the decimal form of 5.5% (note how 5.5% = 5.5/100 = 0.055)
n = 4 means we compound 4 times a year, in other words, quarterly
t = 7 years pass by


Let's plug those mentioned values into the formula. Solve for P.


A = P*(1+r/n)^(n*t)
10000 = P*(1+0.055/4)^(4*7)
10000 = P*(1+0.01375)^(28)
10000 = P*(1.01375)^(28)
10000 = P*1.46576478021002
1.46576478021002*P = 10000
P = 10000/1.46576478021002
P = 6,822.37705190812
P = 6,822.38


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Answer: <font color=red>6822.38 dollars</font>


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Part (b)


Whatever we found back in part (a) represents the amount needed to be put aside to save back to $10,000. The rest can be spent. 
Subtract the result found in part (a) from 10,000 to get: 10,000 - 6,822.38 = 3,177.62


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Answer: <font color=red>3177.62 dollars</font>


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