A company will need $30,000 in 8 years for a new addition. To meet this goal, the company deposits money in an account today that pays 4% annual interest compounded quarterly. Find the amount that should be invested to total $30,000 in 8 years.

where A(t) is the amount after the investment time is over, P is the initial amount invested (what we are looking for), r is the interest rate in decimal form, n is the number of times it compounds per year, and t is the time in years. Fillling in:

[tex]30,000=P(1+\frac{.04}{4})^{(4)(8)}[/tex] and simplifying a bit:

[tex]30,000=P(1+.01)^{32}[/tex] and some more:

30,000 = P(1.374940697)

P = $21,819.12

A company will need ​$30,000 in 8 years for a new addition. To meet this​ goal, the company deposits money in an account today that pays 4​% annual interest compounded quarterly. Find the amount that should be invested to total ​$30,000 in 8 years.

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A company will need $30,000 in 8 years for a new addition. To meet this goal, the company deposits money in an account today that pays 4% annual interest compounded quarterly. Find the amount that should be invested to total $30,000 in 8 years.