Question

ann deposits $70,000 into an account that pays 2% interest per year, compounded annually. jim deposits $70,000 into an account that also pays 2% per year. but it is simple interest. find the interest ann and jim 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 ann earns (interest compounded annually)	interest jim earns (simple interest)	who earns more interest?
second	$\square$	$\square$	select
third	$\square$	$\square$	select

Explanation:

Step1: Calculate Ann's interest (compound interest)

Compound Interest formula: \( A = P(1 + r)^n \), Interest \( I = A - P \)
First year:
\( P = 70000 \), \( r = 0.02 \), \( n = 1 \)
\( A_1 = 70000(1 + 0.02)^1 = 70000\times1.02 = 71400 \)
\( I_{Ann1} = 71400 - 70000 = 1400 \)
Second year:
\( P = 71400 \), \( r = 0.02 \), \( n = 1 \)
\( A_2 = 71400(1 + 0.02)^1 = 71400\times1.02 = 72828 \)
\( I_{Ann2} = 72828 - 71400 = 1428 \)
Third year:
\( P = 72828 \), \( r = 0.02 \), \( n = 1 \)
\( A_3 = 72828(1 + 0.02)^1 = 72828\times1.02 = 74284.56 \)
\( I_{Ann3} = 74284.56 - 72828 = 1456.56 \)

Step2: Calculate Jim's interest (simple interest)

Simple Interest formula: \( I = P\times r\times t \)
First year:
\( P = 70000 \), \( r = 0.02 \), \( t = 1 \)
\( I_{Jim1} = 70000\times0.02\times1 = 1400 \)
Second year:
\( P = 70000 \), \( r = 0.02 \), \( t = 1 \)
\( I_{Jim2} = 70000\times0.02\times1 = 1400 \)
Third year:
\( P = 70000 \), \( r = 0.02 \), \( t = 1 \)
\( I_{Jim3} = 70000\times0.02\times1 = 1400 \)

Step3: Compare interests each year

First year: \( I_{Ann1} = 1400 \), \( I_{Jim1} = 1400 \) → Equal
Second year: \( I_{Ann2} = 1428 \), \( I_{Jim2} = 1400 \) → Ann
Third year: \( I_{Ann3} = 1456.56 \), \( I_{Jim3} = 1400 \) → Ann

Answer:

Interest Ann earns (compounded annually)

• First: $1400$
• Second: $1428$
• Third: $1456.56$

Interest Jim earns (simple interest)

• First: $1400$
• Second: $1400$
• Third: $1400$

Who earns more interest?

• First: Equal
• Second: Ann
• Third: Ann