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

#1**+1 **

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.

P.S. I might be wrong

Mathhemathh
Oct 26, 2017

#3**0 **

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