Sarah deposits $250 into an annuity due at the beginning of every 6-month period for 9 years. The account earns an annual 6% compounded semi

Question

Sarah deposits $250 into an annuity due at the beginning of every 6-month period for 9 years. The account earns an annual 6% compounded semiannually. What is the future value of the annuity after 9 years? How much interest did she earn?

in progress 0
Amaya 1 week 2021-09-08T02:30:22+00:00 1 Answer 0

Answers ( )

    0
    2021-09-08T02:32:07+00:00

    Answer: she earned $6007.5

    Step-by-step explanation:

    We would apply the formula for determining future value involving deposits at constant intervals. It is expressed as

    S = R[{(1 + r)^n – 1)}/r][1 + r]

    Where

    S represents the future value of the investment.

    R represents the regular payments made(could be weekly, monthly)

    r = represents interest rate/number of interval payments.

    n represents the total number of payments made.

    From the information given,

    R = $250

    r = 0.06/2 = 0.03

    n = 2 × 9= 18

    Therefore,

    S = 250[{(1 + 0.03)^18 – 1)}/0.03][1 + 0.03]

    S = 250[{(1.03)^18 – 1)}/0.03][1.03]

    S = 250[{(1.7 – 1)}/0.03][1.03]

    S = 250[{(0.7)}/0.03][1.03]

    S = 250[23.3][1.03]

    S = 250 × 24.03

    S = $6007.5

Leave an answer

45:7+7-4:2-5:5*4+35:2 =? ( )