Question

if i invest 300 dollars a month, compunding monthly at an interest rate of 7.5% for 40 years, how much money would i have

Answer 1

To find out how much money you would have after investing $300 a month at an interest rate of 7.5% compounded monthly for 40 years, you can use the future value of a series formula:

\[
FV = P \times \frac{(1 + r)^n - 1}{r}
\]

Where:
- \( FV \) = future value of the investment
- \( P \) = monthly investment amount
- \( r \) = monthly interest rate (annual rate / 12)
- \( n \) = total number of investments (number of months)

Given:
- \( P = 300 \)
- Annual interest rate = 7.5%, so monthly interest rate \( r = \frac{7.5\%}{12} = 0.00625 \)
- Total investment duration = 40 years, so \( n = 40 \times 12 = 480 \) months

Plugging these values into the formula, we get:

\[
FV = 300 \times \frac{(1 + 0.00625)^{480} - 1}{0.00625}
\]

Now, calculating step-by-step:

1. Calculate \( (1 + r)^{n} \):
\[
(1 + 0.00625)^{480} \approx 14.80020267
\]

2. Now substitute this into the formula:
\[
FV = 300 \times \frac{14.80020267 - 1}{0.00625}
\]
\[
FV = 300 \times \frac{13.80020267}{0.00625}
\]
\[
FV = 300 \times 2208.0324272
\]
\[
FV \approx 662409.73
\]

So, after 40 years of investing $300 a month at an interest rate of 7.5% compounded monthly, you would have approximately **$662,409.73**.