in 15 years Pam hope to have $30,000to make a down payment on a house. how much would she need to invest right now in a mutual fund that earns 8% annual interest in order to have enough for her down payment in 15 years

In which E is the amount of interest earned, P is the principal(the initial amount of money), I is the interest rate(yearly, as a decimal) and t is the time.

After t years, the total amount of money is:

[tex]T = E + P[/tex]

In this question:

In 15 years, so [tex]t = 15[/tex]

She wants to have $30,000, so [tex]T = 30000[/tex]

8% interest, so [tex]I = 0.08[/tex]

We have to find P.

[tex]T = E + P[/tex]

[tex]30000 = E + P[/tex]

[tex]E = 30000 - P[/tex]

Replacing:

[tex]E = P*I*t[/tex]

[tex]30000 - P = P*0.08*15[/tex]

[tex]30000 - P = 1.2P[/tex]

[tex]2.2P = 30000[/tex]

[tex]P = \frac{30000}{2.2}[/tex]

[tex]P = 13636.36[/tex]

She needs to invest $13,636.36 right now

in 15 years Pam hope to have $30,000to make a down payment on a house. how much would she need to invest right now in a mutual fund that earns 8% annual interest in order to have enough for her down payment in 15 years​

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in 15 years Pam hope to have $30,000to make a down payment on a house. how much would she need to invest right now in a mutual fund that earns 8% annual interest in order to have enough for her down payment in 15 years