Question

nicole deposits $30,000 into an account that pays simple interest at a rate of 2% per year. chris deposits $30,000 into an account that also pays 2% interest per year. but it is compounded annually. find the interest nicole and chris 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.

Explanation:

Step1: Calculate Nicole's simple - interest formula

The simple - interest formula is $I = Prt$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), and $t$ is the time in years. Given $P=\$30000$, $r = 0.02$.

Step2: Calculate Nicole's first - year interest

For $t = 1$:
$I_{Nicole1}=30000\times0.02\times1=\$600$

Step3: Calculate Nicole's second - year interest

For $t = 2$:
$I_{Nicole2}=30000\times0.02\times1=\$600$ (since simple interest is constant each year with no changes in principal)

Step4: Calculate Nicole's third - year interest

For $t = 3$:
$I_{Nicole3}=30000\times0.02\times1=\$600$

Step5: Calculate Chris's compound - interest formula

The compound - interest formula is $A=P(1 + r)^t$, where $A$ is the amount of money accumulated after $n$ years, including interest, $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), and $t$ is the number of years. The interest earned $I=A - P$.

Step6: Calculate Chris's first - year interest

For $t = 1$:
$A_1=30000(1 + 0.02)^1=30000\times1.02=\$30600$
$I_{Chris1}=30600 - 30000=\$600$

Step7: Calculate Chris's second - year interest

For $t = 2$:
$A_2=30000(1 + 0.02)^2=30000\times1.02^2=30000\times1.0404=\$31212$
$I_{Chris2}=31212 - 30600=\$612$

Step8: Calculate Chris's third - year interest

For $t = 3$:
$A_3=30000(1 + 0.02)^3=30000\times1.02^3=30000\times1.061208=\$31836.24$
$I_{Chris3}=31836.24 - 31212=\$624.24$

Answer:

Year	Interest Nicole earns (Simple Interest)	Interest Chris earns (Interest compounded annually)	Who earns more interest?
Second	$\$600$	$\$612$	Chris earns more.
Third	$\$600$	$\$624.24$	Chris earns more.