What lump sum do parents need to deposit in an account earning 9%, compounded monthly, so that it will grow to $100,000 for their son’s coll

Question

What lump sum do parents need to deposit in an account earning 9%, compounded monthly, so that it will grow to $100,000 for their son’s college fund in 13 years? (Round your answer to the nearest cent.)

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Arya 4 weeks 2021-12-26T10:42:18+00:00 1 Answer 0 views 0

Answers ( )

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    2021-12-26T10:43:35+00:00

    Answer:

    They need to deposit $31,172.49

    Step-by-step explanation:

    The compound interest formula is given by:

    A = P(1 + \frac{r}{n})^{nt}

    Where A is the amount of money, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time the money is invested or borrowed for, in years.

    In this problem

    We want to find P for which A = 100000 when r = 0.09, n = 12, t = 13

    So

    A = P(1 + \frac{r}{n})^{nt}

    100000 = P(1 + \frac{0.09}{12})^{12*13}

    3.208P = 100000

    P = \frac{100000}{3.208}

    P = 31172.49

    They need to deposit $31,172.49

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