Question

if you had 22400 and it goes down by by 6.75% each year how much would you have in 9 years

Answer 1

To find out how much you would have after 9 years when an initial amount of $22,400 decreases by 6.75% each year, you can use the formula for exponential decay:

\[
A = P \times (1 - r)^t
\]

where:
- \(A\) is the amount after time \(t\),
- \(P\) is the initial amount,
- \(r\) is the rate of decrease (as a decimal),
- \(t\) is the number of years.

In this case:
- \(P = 22,400\)
- \(r = 6.75\% = 0.0675\)
- \(t = 9\)

Now, plug in the values:

\[
A = 22,400 \times (1 - 0.0675)^9
\]

Calculating \(1 - 0.0675\):

\[
1 - 0.0675 = 0.9325
\]

Now, raise this to the power of 9:

\[
(0.9325)^9 \approx 0.5322
\]

Now, multiply by the initial amount:

\[
A \approx 22,400 \times 0.5322 \approx 11,935.68
\]

Therefore, after 9 years, you would have approximately **$11,935.68**.