Question

lisa deposits $10,000 into an account that pays 4% interest per year, compounded annually.
scott deposits $10,000 into an account that also pays 4% per year. but it is simple interest.
find the interest lisa and scott 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 lisa earns (interest compounded annually)	interest scott earns (simple interest)	who earns more interest?
second	$□	$□	select ▾
third	$□	$□	select ▾

Explanation:

Step1: Recall Formulas

• Simple Interest (Scott): \( I = P \times r \times t \), where \( P = 10000 \), \( r = 0.04 \), \( t = 1,2,3 \)
• Compound Interest (Lisa): \( A = P(1 + r)^t \), Interest \( I = A - P \)

Step1: First Year

Scott (Simple Interest)

\( I = 10000 \times 0.04 \times 1 = 400 \)

Lisa (Compound Interest)

\( A = 10000(1 + 0.04)^1 = 10400 \), \( I = 10400 - 10000 = 400 \)

Who earns more: Equal

Step2: Second Year

Scott (Simple Interest)

\( I = 10000 \times 0.04 \times 1 = 400 \) (same as first year, simple interest is constant per year)

Lisa (Compound Interest)

\( A = 10000(1 + 0.04)^2 = 10000 \times 1.0816 = 10816 \), \( I = 10816 - 10400 = 416 \) (interest on previous amount)

Who earns more: Lisa

Step3: Third Year

Scott (Simple Interest)

\( I = 10000 \times 0.04 \times 1 = 400 \)

Lisa (Compound Interest)

\( A = 10000(1 + 0.04)^3 = 10000 \times 1.124864 = 11248.64 \), \( I = 11248.64 - 10816 = 432.64 \)

Who earns more: Lisa

Answer:

Year	Interest Lisa earns	Interest Scott earns	Who earns more interest?
Second	$416$	$400$	Lisa
Third	$432.64$	$400$	Lisa