Question

Lillian is going to invest in an account paying an interest rate of 5.7% compounded continuously. 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?

Answer 1

The amount Lilian needs to invest is $5,160

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;

`A = P \cdot \left(1 + (r)/(n) \right)^(n\cdot t)`

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;

`7,600 = P \cdot \left(1 + 0.057 \right)^(7)`

∴ 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