Question

ive years from today, you plan to invest $4,900 for 8 additional years at 7.8 percent compounded annually. How much will you have in your account 13 years from today?


Multiple Choice

$13,008.88


$8,936.06


$9,322.51


$7,133.29


$9,439.74

Answer 1

To find out how much you will have in your account 13 years from today after investing $4,900 for 8 additional years at an interest rate of 7.8% compounded annually, you can use the formula for compound interest:

\[
A = P(1 + r)^n
\]

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 years the money is invested or borrowed.

In this situation:
- \( P = 4900 \)
- \( r = 7.8\% = 0.078 \)
- \( n = 8 \) (the number of years you are investing after the initial 5 years)

Now, plug in the values:

\[
A = 4900(1 + 0.078)^8
\]
\[
A = 4900(1.078)^8
\]

Calculating \( (1.078)^8 \):

\[
(1.078)^8 \approx 1.747422
\]

Now, multiply this by the principal:

\[
A \approx 4900 \times 1.747422 \approx 8567.76
\]

So, after 13 years, you will have approximately $8,567.76 in your account.

Now let's look at the multiple choices, as none of the options seem to match. There may have been an error in calculating \( (1.078)^8 \). Let's calculate it more closely:

Using accurate calculation:

\[
(1.078)^8 \approx 1.85093
\]

Now multiply:

\[
A \approx 4900 \times 1.85093 \approx 9080.56
\]

So it appears \( 4900 \times 1.85093 \approx 9080.56 \).

With this, we can conclude that you will have approximately $9,080.56 after 13 years.

However, none of the available options exactly match, but among the closest ones is:

\[
\text{Option: } \textbf{$9,322.51$}
\]

For the most accurate selection or correction, you can check if we misunderstood parameters. If everything seems accurate, check these numerical matches with accurate calculators or tools.