Questions: (a) Assuming no withdrawals are made, how much money is in Scott's account after 3 years? (b) How much interest is earned on Scott's investment after 1 year?

Solution Steps

To solve these questions, we need to understand the concept of compound interest. The formula for compound interest is:

\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]

where:

• \( A \) is the amount of money accumulated after n years, including interest.
• \( P \) is the principal amount (the initial amount of money).
• \( r \) is the annual interest rate (decimal).
• \( n \) is the number of times that interest is compounded per year.
• \( t \) is the time the money is invested for in years.

(a) To find the amount in Scott's account after 3 years, we will use the compound interest formula with the given values for \( P \), \( r \), \( n \), and \( t = 3 \).

(b) To find the interest earned after 1 year, we will calculate the total amount after 1 year using the compound interest formula and subtract the principal amount from it.

Using the compound interest formula:

\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]

we substitute the values \( P = 1000 \), \( r = 0.05 \), \( n = 1 \), and \( t = 3 \):

\[ A = 1000 \left(1 + \frac{0.05}{1}\right)^{1 \cdot 3} = 1000 \left(1.05\right)^{3} \approx 1157.625 \]

Thus, the amount in Scott's account after 3 years is approximately \( 1157.625 \).

Using the same formula for \( t = 1 \):

\[ A = 1000 \left(1 + \frac{0.05}{1}\right)^{1 \cdot 1} = 1000 \left(1.05\right)^{1} = 1000 \cdot 1.05 = 1050.0 \]

The interest earned after 1 year is given by:

\[ \text{Interest} = A - P = 1050.0 - 1000 = 50.0 \]

Final Answer