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Consider the two savings plans below. Compare the balances in each plan after 7 years. Which person deposited more money in the​ plan? Which of the two investment strategies is​ better? Yolanda deposits ​$600 per month in an account with an APR of 4​%, while Zach deposits ​$7200 at the end of each year in an account with an APR of 4​%.The balance in​ Yolanda's saving plan after 7 years was ​$

.

​(Round the final answer to the nearest cent as needed. Round all intermediate values to seven decimal places as​ needed.)

Guest Oct 26, 2017
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4+0 Answers

 #1
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Assuming month = 30 days.

 

Yolanda's savings after n years = \(Y_n\)

Zach's savings after n years = \(Z_n\)

 

Yolanda's DPR ==> \(DPR={APR\over365}={4\%\over365}=.0109589041096\%\)

Zach's DPR is the same.

 

Monthly percentage rate of both accounts ==> \(.0109589041096\%*30=0.328767123288\%\)

 

Yolanda will have total savings of \($(600*7*12+600*0.328767123288\%*7*12)\) 600 being the monthly deposit, 7*12 being the total months in 7 years, and 600*0.328767123288% being the monthly percentage rate. Computing, we get \(Y_7=$50565.6986301\).

Zach will have total savings of \($(7200*7+7200*7*4\%)\) 7200 being the yearly deposit, 7 being the number of years, 7200*7*4% being the interest after 7 years. Computing, we get \(Z_7=$52416\).

 

Comparing the two, we see that Zach's investment strategy is more effective. wink

 

P.S. I might be wrong

Mathhemathh  Oct 26, 2017
edited by Mathhemathh  Oct 26, 2017
 #2
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Yeah thanks both wrong though! Thank you for trying! 

Guest Oct 26, 2017
 #4
avatar+91053 
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If you know that they are wrong then you must know what the answer is already.

So why do you give people here less information than what you have been given?

Melody  Oct 26, 2017
 #3
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Well, this is what happens when you give wrong numbers in your questions!!!!,

 

Formula: FV =P x {[1 + R]^N -1 / R}

                FV =600 x {[1 + 0.04/12]^(7*12) - 1 / (0.04/12)}

                FV =600 x {[1.003333333]^84 - 1 / (0.003333333)}

                FV =600 x {[1.3225138..] - 1 / (0.003333333)}

                FV =600 x            96.7541591656..........

                FV =$58,052.50 - Balance in Yolanda's account after 7 years.

 

 Zach's Account:

              FV =7,200 x {{1+0.04]^7 -1 / 0.04}

              FV =$58,867.72 - Balance in Zach's account after 7 years.

Guest Oct 26, 2017

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