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The amount to which $100 will grow in t years with an interest rate (r) compounded annually is given by the polynomial function A:

 

A(r) = $100(1 + r)t 

 

a) Find the amount to which $100 will grow in 2 years at 6%.

 

b) The amount to which $100 will grow in 4 years at 17%.

GAMEMASTERX40  Sep 20, 2018
 #1
avatar+2248 
+2

Hi, Rick!

 

When the question asks you to "[f]ind the amount to which $100 will grow in 2 years at 6%," the question is directly telling you the values of the unknowns, and t.

 

  • r is the interest rate, which the problem states as 6%. When you substitute this into the equation, though, 6% will be converted to a decimal.
  • t is the number of years, which the problem states as 2

The only part left to do is to substitute these values into the equation and solve.

 

\(A(r,t)=100(1+r)^t\\ A(0.06,2)=100(1+0.06)^2\\ A(0.06,2)=\$112.36\)

 

See if you can do the next one.

TheXSquaredFactor  Sep 20, 2018
 #2
avatar+991 
+2

Hey, TheXSquaredFactor! I did the work with the frist one and I got the right answer so now I understand. Then I did the same method with the next one and this what I got:

 

A(r,t) = 100(1+r)^t

A(0.17,4) = 100(1+0.17)^4

A(0.17,4) = $187.388721

 

I suppose that this is right, but I don't know if I have to round the answer.

 

Thanks

GAMEMASTERX40  Sep 20, 2018
 #3
avatar+2248 
+1

Good job, Rick! You should absolutely round to the nearest hundredth place. The context of this problem deals with money, and the smallest modern currency only comes in denominations of cents. Fitting this context requires you to round. 

TheXSquaredFactor  Sep 20, 2018
 #4
avatar+991 
+1

There, the answer should be $187.39

 

Thanks so much!

GAMEMASTERX40  Sep 20, 2018

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