$12: 57$ 40 MM150 Survey of Mathematics Brylon Beckworth $\quad 07 / 16 / 23$ 2:57 PM (?) $\equiv$ Homework: Unit 6 Lab Homework Question list Question 1 Question 2 Question 3 Question 4 Question 5 Question 6 Question 7 Question 8 Question 9 Question 10 Question 11 Question 12 Question 13 Question 14 Question 15 Question 16 K Will you earn more interest in one year by depositing $\$ 3000$ in a simple interest account that pays $7 \%$ or in an account that pays $6.9 \%$ interest compounded daily? How much more interest will you earn? Click the icon to view some finance formulas. In which account will you earn more interest? Select the correct choice below and fill in the answer box within your choice. (Round to the nearest dollar as needed.) A. You will earn $\$$ more interest in the compoundinterest account than in the simpleinterest account. B. You will earn $\$$ more interest in the simpleinterest account than in the compoundinterest account. AA View an example Get more help * Clear all Check answer
Solution
Step 1 ：Given that the principal amount (P) is $3000, the rate of interest for the simple interest account (R) is 0.07, and the time (T) is 1 year, we can calculate the simple interest using the formula I = PRT. This gives us a simple interest of $210.
Step 2 ：Next, we calculate the compound interest for an account with the same principal amount (P) of $3000, an annual interest rate (r) of 0.069, compounded daily (n = 365), and for the same time period (t) of 1 year. Using the formula A = P(1 + r/n)^(nt), we find that the compound interest is approximately $214.29.
Step 3 ：By comparing the two amounts, we can see that the compound interest account earns more interest than the simple interest account.
Step 4 ：To find out how much more interest is earned, we subtract the simple interest from the compound interest. This gives us a difference of approximately $4.29.
Step 5 ：Thus, the compound interest account earns approximately $4.29 more interest than the simple interest account in one year. So, the final answer is \(\boxed{4.29}\).
