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

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

Answer 2

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

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+(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* 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