May won $1000 She invested in an account paying 9% interest rate compounded yearly. a(t)=1,000(1.09)^t. Where a is the amount in the account after t years. If she uses it 10 years later determine the situation

Answer 1

To determine the amount in May's account after 10 years with her investment compounded yearly at a 9% interest rate, we can use the formula provided:

\[ a(t) = 1000(1.09)^t \]

where:

• \( a(t) \) is the amount in the account after \( t \) years,
• 1000 is the initial investment,
• 1.09 is the factor representing the original investment plus the interest rate,
• \( t \) is the number of years.

Now, substituting \( t = 10 \) into the formula:

\[ a(10) = 1000(1.09)^{10} \]

Now, we need to calculate \( (1.09)^{10} \):

\[ (1.09)^{10} \approx 2.36736 \]

Now, plug this back into the equation:

\[ a(10) = 1000 \times 2.36736 \approx 2367.36 \]

So, the amount in May's account after 10 years will be approximately $2367.36.