Questions: Karen deposits 10,000 into an account that pays simple interest at a rate of 2% per year. David deposits 10,000 into an account that also pays 2% interest per year. But it is compounded annually. Find the interest Karen and David 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.

Karen deposits 10,000 into an account that pays simple interest at a rate of 2% per year.
David deposits 10,000 into an account that also pays 2% interest per year. But it is compounded annually.
Find the interest Karen and David 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.

Transcript text: Karen deposits $10,000 into an account that pays simple interest at a rate of 2% per year. David deposits $10,000 into an account that also pays 2% interest per year. But it is compounded annually. Find the interest Karen and David 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.

Solution

Solution Steps

Step 1: Simple Interest Calculation

Using the formula $\text{Simple Interest} = P \times r \times t$, where $P = 10000$, $r = 0.02$, and $t = 3$ years, we calculate the simple interest as $600$.

Step 2: Compound Interest Calculation

Using the formula $\text{Compound Interest} = P \times (1 + \frac{r}{n})^{n \times t} - P$, with $n=1$ for annual compounding, we calculate the compound interest as $612.08$.

Step 3: Comparison

Compound interest earns more over 3 years, with a total interest of $612.08$ compared to simple interest's $600$.