Consider the two savings plans below. Compare the balances in each plan after 10 years. Which person deposited more money in the plan? Which of the two investment strategies is better? Yolanda deposits $200 per month in an account with an APR of 3%, while Zach deposits $2400 at the end of each year in an account with an APR of 3%.
Accepted Solution
A:
Answer:Step-by-step explanation:Yolanda deposits $200 per month, so her total investments are = 200 × 12 × 10 = $24,000After 10 years, the balance in Yolanda's account :[tex]A=PMT\times\frac{[1+(\frac{APR}{n})]^{(ny)}-1}{(\frac{APR}{n} )}[/tex][tex]=200\times\frac{[1+(\frac{0.03}{12})]^{(12\times 10)}-1}{(\frac{0.03}{12})}[/tex][tex]=200\times(\frac{1.0025^{120}-1}{\frac{0.03}{12} })[/tex]= 200 × 139.741419= 27,948.283775 ≈ $27,948.28Zach deposits $2400 per year, so his total investments are = 2400 × 10 = $24,000[tex]=2400\times\frac{[1+(\frac{0.03}{1})]^{(1\times 10)}-1}{(\frac{0.03}{1})}[/tex][tex]=2400\times\frac{[1+(\frac{0.03}{1})]^{(10)}-1}{0.03}[/tex][tex]=2400(\frac{1.03^{10}-1}{0.03} )[/tex]= 2400 × 11.463879= 27513.310348 ≈ $27,513.31Yolanda's strategies is better because she would receive 27,948.28 while Zach would receive 27,513.31.