BJ’s goal is to have $50,000 saved at the end of Year 5. At the end of Year 2, they can add $7,500 to their savings but they want to deposit

Question

BJ’s goal is to have $50,000 saved at the end of Year 5. At the end of Year 2, they can add $7,500 to their savings but they want to deposit the remainder they need to reach their goal today, Year 0, as a lump sum deposit. If they can earn 4.5 percent, how much must they deposit today

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Clara 1 month 2021-10-18T14:47:18+00:00 1 Answer 0 views 0

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    0
    2021-10-18T14:48:29+00:00

    Answer:

    $33534.73

    Step-by-step explanation:

    Let the lump sum be P.

    The interest, I, on a rate, R%, per annum after T years is given by

    I = PRT/100

    The amount, A, is

    A = P + I = P(1 + \frac{RT}{100})

    After 2 years at 4.5% interest rate, the amount is

    A = P(1+\dfrac{4.5\times2}{100}=1.09P

    $7500 is added after 2 years. The principal for the beginning of the third year is then

    1.09P + 7500

    The amount after the next 3 years is

    A = (1.09P + 7500)\left(1+\dfrac{4.5\times3}{100}\right)=(1.09P + 7500)\times1.135

    This is the amount expected to be saved.

    50000=(1.09P + 7500)\times1.135

    Solving for P, we have

    1.09P + 7500 = 44052.86

    1.09P = 36552.86

    P = 33534.23

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