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Sagot :
Answer:
The size of the investment after 40 years is of $74,872.
Step-by-step explanation:
Continuous compounding:
The amount of money, in continuous compounding, after t years, is given by:
[tex]y(t) = y(0)(1+r)^t[/tex]
In which y(0) is the initial investment and r is the interest rate, as a decimal.
You decide to continuously invest $5000 of your income each year in a risk-free investment with a 7% yearly interest rate compounded continuously.
This means that [tex]y(0) = 5000, r = 0.07[/tex]. So
[tex]y(t) = y(0)(1+r)^t[/tex]
[tex]y(t) = 5000(1+0.07)^t[/tex]
[tex]y(t) = 5000(1.07)^t[/tex]
What is the size of your investment after 40 years?
This is y(40), that is, y when t = 40. So
[tex]y(t) = 5000(1.07)^t[/tex]
[tex]y(40) = 5000(1.07)^{40}[/tex]
[tex]y(40) = 74872[/tex]
The size of the investment after 40 years is of $74,872.
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