Answer:
She has to invest $5,160 for the value of the account to reach $7,600 in 7 years.
Step-by-step explanation:
Continuous compounding:
The amount of money earned, after t years, in continuous compounding, is given by:
[tex]A(t) = A(0)(1+r)^t[/tex]
In which A(0) is the value of the initial investment and r is the interest rate, as a decimal.
Lillian is going to invest in an account paying an interest rate of 5.7% compounded continuously.
This means that [tex]r = 0.057[/tex]
How much would Lillian need to invest, to the nearest ten dollars, for the value of the account to reach $7,600 in 7 years?
We have to find A(0) when [tex]A(t) = 7600, t = 7[/tex]
So
[tex]A(t) = A(0)(1+r)^t[/tex]
[tex]7600 = A(0)(1+0.057)^7[/tex]
[tex]A(0) = \frac{7600}{(1.057)^7}[/tex]
[tex]A(0) = 5156[/tex]
To the nearest ten dollars, she has to invest $5,160 for the value of the account to reach $7,600 in 7 years.
