MATH SOLVE

4 months ago

Q:
# Please answer quickly for 5 stars and brainliest!! Emilio wants to invest $15,820 that he just received as a prize from a contest he entered. He researches certificates of deposit (CDs) at two different banks. The details for his two best options are in the table below. Both CDs earn compound interest, which you worked on in Exponential Growth & Decay. When interest is compounded, it is added to the account’s principal to become part of the money that earns interest. 1. Determine which investment will earn Emilio more interest. First Bank or Bank West2. How much more interest will he earn with that investment?

Accepted Solution

A:

Answer:Bank West$242.82Step-by-step explanation:To find which bank will yield more interest for Emilio, we can solve for the interest of each bank by using the Compound interest formula:[tex]A=P(1+\dfrac{r}{n})^{nt}[/tex]For the Bank West we have:n = 4 Quarterlyt = 6 yearsr = 3.8% or 0.038P = 15820Let's substitute them in the formula.[tex]A=15820(1+\dfrac{0.038}{4})^{4(6)}[/tex][tex]A=15820(1+\dfrac{0.038}{4})^{24}[/tex][tex]A=15820(1+0.0095)^{24}[/tex][tex]A=15820(1.0095)^{24}[/tex][tex]A=19849.89[/tex]Now let's solve for the Interest. We subtract our total amount to the principal amount.Interest = 19849.89 - 15820Interest = 4029.89Now let's solve for the First Bank.n = 12 Monthlyt = 5 yearsr = 4.3% or 0.043P = 15820Let's substitute them in the formula.[tex]A=15820(1+\dfrac{0.043}{12})^{12(5)}[/tex][tex]A=15820(1+\dfrac{0.043}{12})^{60}[/tex][tex]A=19607.07[/tex]Now for the interest:Interest = 19607.07 - 15820Interest = 3787.07This gives us:Bank West Interest = $4029.89First Bank Interest = $3787.07So Bank West will earn more interest than First Bank.To find how much more interest we subtract the interest of Bank West to First Bank.4029.89 - 3787.07 = $242.82