Question

christine deposits $80,000 into an account that pays 6% interest per year, compounded annually.kevin deposits $80,000 into an account that also pays 6% per year. but it is simple interest.find the interest christine and kevin earn during each of the first three years.then decide who earns more interest for each year.assume there are no withdrawals and no additional deposits.| year | interest christine earns (interest compounded annually) | interest kevin earns (simple interest) | who earns more interest? || ---- | ---- | ---- | ---- || first | $$$ $square$ | $$$ $square$ | select $\boldsymbol{vee}$ || second | LXB1$ $square$ | select $\boldsymbol{vee}$ || third | $$$ $square$ | $$$ $square$ | select $\boldsymbol{vee}$ |

Explanation:

Step1: Calculate Christine's Year1 interest

Annual compound interest: $I = P \times r$
$I_1 = 80000 \times 0.06 = 4800$

Step2: Calculate Christine's Year2 interest

New principal: $P_2 = 80000 + 4800 = 84800$
$I_2 = 84800 \times 0.06 = 5088$

Step3: Calculate Christine's Year3 interest

New principal: $P_3 = 84800 + 5088 = 89888$
$I_3 = 89888 \times 0.06 = 5393.28$

Step4: Calculate Kevin's annual interest

Simple interest: $I = P \times r$
$I_{\text{each}} = 80000 \times 0.06 = 4800$

Step5: Compare annual interest

Year1: $4800 = 4800$ (equal)
Year2: $5088 > 4800$ (Christine more)
Year3: $5393.28 > 4800$ (Christine more)

Answer:

Year	Interest Christine earns (Interest compounded annually)	Interest Kevin earns (Simple interest)	Who earns more interest?
Second	$\$5088$	$\$4800$	Christine
Third	$\$5393.28$	$\$4800$	Christine