Question

jason deposits $300 into an account that earns 5% annual compound interest. sean deposits $315 into an account that earns 6% annual simple interest. who will have more at the end of 15 years?

Explanation:

Step1: Calculate Jason's amount (compound interest)

The formula for compound interest is $A = P(1 + r)^t$, where $P$ is principal, $r$ is rate (decimal), $t$ is time.
$P = 300$, $r = 0.05$, $t = 15$.
$A_{Jason} = 300(1 + 0.05)^{15}$
First, calculate $(1.05)^{15} \approx 2.078928$.
Then, $A_{Jason} = 300 \times 2.078928 \approx 623.68$.

Step2: Calculate Sean's amount (simple interest)

The formula for simple interest is $A = P(1 + rt)$, where $P$ is principal, $r$ is rate, $t$ is time.
$P = 315$, $r = 0.06$, $t = 15$.
$A_{Sean} = 315(1 + 0.06 \times 15)$
First, calculate $0.06 \times 15 = 0.9$. Then, $1 + 0.9 = 1.9$.
$A_{Sean} = 315 \times 1.9 = 598.5$.

Step3: Compare the two amounts

Jason's amount: ~$623.68$, Sean's amount: $598.5$.
Since $623.68 > 598.5$, Jason has more.

Answer:

Jason will have more at the end of 15 years.