Questions: If you invest 5,000 dollars in an investment which returns 7% annually, how much will that investment be worth in 6 years? (start in year 0)

Solution Steps

To solve this problem, we need to calculate the future value of an investment using the formula for compound interest. The formula is:

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

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.

In this case, the interest is compounded annually, so \( n = 1 \).

We start with the following values:

• Principal amount \( P = 5000 \)
• Annual interest rate \( r = 0.07 \)
• Number of times interest is compounded per year \( n = 1 \)
• Time in years \( t = 6 \)

We use the compound interest formula:

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

Substituting the identified values into the formula:

\[ A = 5000 \left(1 + \frac{0.07}{1}\right)^{1 \cdot 6} \]

Calculating the expression:

\[ A = 5000 \left(1 + 0.07\right)^{6} = 5000 \left(1.07\right)^{6} \]

Calculating \( (1.07)^{6} \):

\[ (1.07)^{6} \approx 1.484812 \]

Now, substituting back to find \( A \):

\[ A \approx 5000 \times 1.484812 \approx 7424.06 \]

Final Answer