Question

Lakisha just won some money in a sweepstakes drawing. She is considering putting her winnings in a long term investment. To the nearest dollar, how much money would Lakisha need to put into an account earning 5% interest compounded annually in order to have $30,000 at the end of 20 years?

Answer 1

Answer: She would need to put approximately $ 11306.684 into the account in order to have $30,000 at the end of 20 years.

Step-by-step explanation:

Let P be the amount of the money she need to put into the account,

Since, the annual rate of interest = 5%

Time = 20 years

Hence, with this compound interest the amount she got after 20 years,

$A=P(1+\frac{5}{100})^{20}$

$\implies A = P(1+0.05)^{20}\implies A = P(1.05)^{20}$

According to the question,

A = $ 30,000

$\implies P(1.05)^{20} = 30000$

$\implies P\times 2.65329770514 = 30000$

$\implies P = 11306.6844862\approx 11306.684$

Hence, She would need to put approximately $ 11306.684 into the account in order to have $30,000 at the end of 20 years

Answer 2

Amount after n years = original amount x interest^(number of years)
30,000 = A x (1.05)²⁰
A = $11,307