If you invest $1,000 per month with a 12% annual rate of return compounded monthly, you would have approximately $31,171.46 after 10 years, $77,510.58 after 20 years, $192,033.23 after 30 years, and $476,116.62 after 40 years.
To calculate the future value of an investment with compound growth, you can use the compound interest formula:
FV=P×(1+r)^nt
Where:
FV is the future value of the investment.
P is the principal amount (initial investment).
r is the annual interest rate (as a decimal).
n is the number of times interest is compounded per year.
t is the number of years the money is invested.
In this case, a monthly investment of $1,000, a 12% annual interest rate, and we'll assume monthly compounding.
Let's calculate for different time periods:
After 10 years (t=10):
FV_10=1000×(1+0.12/12)^12×10
After 20 years (t=20):
FV_20=1000×(1+0.12/12)^12×20
After 30 years (t=30):
FV_30 =1000×(1+0.12/12)^12×30
After 40 years (t=40):
FV_40 =1000×(1+0.12/12)^12×40
Now let's calculate these values:
FV_10 =1000×(1+0.01)^120 ≈$31,171.46
FV_20=1000×(1+0.01)^240 ≈$77,510.58
FV_30 =1000×(1+0.01)^360 ≈$192,033.23
FV_40 =1000×(1+0.01)^480 ≈$476,116.62
So, if you invest $1,000 per month with a 12% annual rate of return compounded monthly, you would have approximately $31,171.46 after 10 years, $77,510.58 after 20 years, $192,033.23 after 30 years, and $476,116.62 after 40 years.
Question
Instead of spending that money on the lottery, consider what would happen if you invested instead—to take advantage of compound growth. If you were to invest that monthly amount 1000 in each month, with a 12% rate of return, how much would you have after 10 years? 20 years? 30 years? 40 years?