Question

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​%.

Answer 1

Answer:

Step-by-step explanation:

Yolanda deposits $200 per month, so her total investments are = 200 × 12 × 10 = $24,000

After 10 years, the balance in Yolanda's account :

$A=PMT\times\frac{[1+(\frac{APR}{n})]^{(ny)}-1}{(\frac{APR}{n} )}$

$=200\times\frac{[1+(\frac{0.03}{12})]^{(12\times 10)}-1}{(\frac{0.03}{12})}$

$=200\times(\frac{1.0025^{120}-1}{\frac{0.03}{12} })$

= 200 × 139.741419

= 27,948.283775 ≈ $27,948.28

Zach deposits $2400 per year, so his total investments are = 2400 × 10 = $24,000

$=2400\times\frac{[1+(\frac{0.03}{1})]^{(1\times 10)}-1}{(\frac{0.03}{1})}$

$=2400\times\frac{[1+(\frac{0.03}{1})]^{(10)}-1}{0.03}$

$=2400(\frac{1.03^{10}-1}{0.03} )$

= 2400 × 11.463879

= 27513.310348 ≈ $27,513.31

Yolanda's strategies is better because she would receive 27,948.28 while Zach would receive 27,513.31.