Part A: To calculate the interest Emily will earn after 2 years, we use the formula for simple interest because the problem does not state compound interest. The formula for simple interest is:
\[ I = P \cdot r \cdot t \]
where \( I \) is the interest earned, \( P \) is the principal amount (the initial amount of money), \( r \) is the annual interest rate, and \( t \) is the time in years.
Given in the problem:
- \( P = \$5000 \)
- \( r = 4\% = 0.04 \) (as a decimal)
- \( t = 2 \) years
Now we'll calculate the interest earned:
\[ I = 5000 \cdot 0.04 \cdot 2 \]
\[ I = 200 \cdot 2 \]
\[ I = \$400 \]
Emily will earn $400 in interest after 2 years.
Part B: To find out how much money Emily will have in total after 2 years, we need to add the original principal to the interest earned.
\[ \text{Total amount} = \text{Principal} + \text{Interest earned} \]
\[ \text{Total amount} = \$5000 + \$400 \]
\[ \text{Total amount} = \$5400 \]
After 2 years, Emily will have a total of $5400 in her savings account if she decides to withdraw the money.
Part C: Whether this is the best investment option for Emily depends on her financial goals, risk tolerance, and the availability of other investment opportunities. Given that Emily wants her money to be available in 2 years, a savings account is a conservative option that provides safety and liquidity. The interest rate is relatively low, but the money is safe and can be easily accessed when needed.
If Emily is looking for low-risk and needs the money in the short term, this could be a suitable investment. However, if she is willing to take on more risk for potentially higher returns, she might consider other options such as stocks or mutual funds, which historically can offer better returns but come with the risk of losing principal. She could also consider a certificate of deposit (CD) that might offer a higher interest rate than a savings account but would require her to leave the money untouched for a certain period.
It is important for Emily to compare the savings account with her other options, considering factors like the interest rates, risk levels, and access to funds to determine the best investment choice for her individual circumstances.
