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MrMuchimi
2 years ago
13

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 f

und that earns 8% annual interest in order to have enough for her down payment in 15 years​
Mathematics
1 answer:
Goryan [66]2 years ago
5 0

Answer:

She needs to invest $13,636.36 right now

Step-by-step explanation:

This is a simple interest problem.

The simple interest formula is given by:

E = P*I*t

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:

T = E + P

In this question:

In 15 years, so t = 15

She wants to have $30,000, so T = 30000

8% interest, so I = 0.08

We have to find P.

T = E + P

30000 = E + P

E = 30000 - P

Replacing:

E = P*I*t

30000 - P = P*0.08*15

30000 - P = 1.2P

2.2P = 30000

P = \frac{30000}{2.2}

P = 13636.36

She needs to invest $13,636.36 right now

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Step-by-step explanation:

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We have

\displaystyle \int_C \vec f \cdot d\vec r = \int_0^{\frac{3\pi}2} \vec f(\vec r(t)) \cdot \dfrac{d\vec r}{dt} \, dt

and

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\vec r(t) = \sin(t)\,\vec\imath + \cos(t)\,\vec\jmath + t\,\vec k \implies \dfrac{d\vec r}{dt} = \cos(t) \, \vec\imath - \sin(t) \, \vec\jmath + \vec k

so the line integral is equilvalent to

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