SOLUTION: A group of workers won the lottery and will each walk away with $10 000. Fred, one of the workers, decides to spend some of the money and save the rest. He wants the money he save

Question 1133089: A group of workers won the lottery and will each walk away with $10 000. Fred, one of the workers, decides to spend some of the money and save the rest. He wants the money he saves to grow back into $10 000 in 7 years. He can invest the money at 5.5% compounded quarterly.

a) How much must he invest to meet his goal.

b) How much money can he afford to spend today?

(I have been working on this problem and i did get for R=4657.65 and i am not sure what they mean by part b.)

Found 2 solutions by jim_thompson5910, addingup:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
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

--------------------

Answer: 6822.38 dollars

====================================================

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

--------------------

Answer: 3177.62 dollars

Answer by addingup(3677) (Show Source): You can put this solution on YOUR website!
Let the amount he invests be x.
x(1+(0.055/4))^(4*7) = 10,000
x*1.466 = 10,000
x = 6,821.30 this is how much he has to invest to have 10,000 in 7 years
10,000 - 6,821.30 = 3,178.70 this is how much he can afford to spend today (and still have 10K in 7 years)
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