Answer:
The amount Lilian needs to invest is $5,160
Step-by-step explanation:
The parameters of the amount Lilian is going to invest in an account are;
The interest rate the account pays = 5.7%
The final amount the investment is expected to reach after the given time period = $7,600
The number of years of the investment = 7 years
The formula for compound interest is presented as follows;
[tex]A = P \cdot \left(1 + \dfrac{r}{n} \right)^{n\cdot t}[/tex]
Where;
A = The final amount = $7,600
P = The amount Lilian is to invest
r = The interest rate = 5.7% = 0.057
n = The number of times the interest is applied per time period = 1
t = The number of period that passes = 7 (years)
Therefore, we get;
[tex]7,600 = P \cdot \left(1 + 0.057 \right)^{7}[/tex]
∴ P = 7,600/(1 + 0.057)⁷ = 5,155.7123754
The amount Lilian needs to invest (rounded to the nearest ten dollars) for the value of the account to reach $7,600 in 7 years, P = $5,160
