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11-74.

Tim wants to invest some money that his grandmother gave him. He has $2000$ and can put it in an account with simple interest or an account with compound interest.

1. The simple interest account is for 5 years with an interest rate of $10\%$. Use the formula $I = P · rt$ to find the interest he earned at the end of five years. How can you use the interest to calculate the total amount in the account at the end of 5 years? What is the total?

Add the interest he earns to his initial principal to find the total amount he would have after 5 years.

$I = (2000)(.1)(5 \text{years})$
$I = 1000$

$\text{Total} = 2000 + 1000 = 3000$

2. The compound interest account is also for 5 years (compounded yearly) at an interest rate of $8\%$. Find the total in the account $\left(A\right)$ using the formula $A = P(1 + r)^t$. What is the total?

$A = 2000(1 + 0.8)^5$

$(1.08)^5 = 1.469$

$A = 2000 (1.469) = 2938.66$

3. Which account is a better investment?

Which account has more money after 5 years?