Your parents will retire in 30 years. They currently have $350,000 saved, and they think they will need $1,450,000 at retirement. What annua

Question

Your parents will retire in 30 years. They currently have $350,000 saved, and they think they will need $1,450,000 at retirement. What annual interest rate must they earn to reach their goal, assuming they don’t save any additional funds? Round your answer to two decimal places.

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Autumn 2 weeks 2021-09-12T21:36:47+00:00 2 Answers 0

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    0
    2021-09-12T21:38:15+00:00

    Answer: the interest rate is 4.86%

    Step-by-step explanation:

    Assuming the interest was compounded annually, we would apply the formula for determining compound interest which is expressed as

    A = P(1+r/n)^nt

    Where

    A = total amount in the account at the end of t years

    r represents the interest rate.

    n represents the periodic interval at which it was compounded.

    P represents the principal or initial amount deposited

    From the information given,

    P = $350000

    A = $1450000

    n = 1 because it was compounded once in a year.

    t = 30 years

    Therefore,.

    1450000 = 350000(1+r/1)^1 × 30

    1450000/350000 = (1 + r)^30

    4.14 = (1 + r)^30

    Taking log of both sides of the equation, it becomes

    Log 4.14 = 30 log(1 + r)

    0.617 = 30 log (1 + r)

    0.0206 = log(1 + r)

    Taking exponent of both sides, it becomes

    10^0.0206 = 10^log(1 + r)

    1 + r = 1.0486

    r = 1.0486 – 1 = 0.0486

    Converting to percentage, it becomes

    r = 0.0486 × 100 = 4.86%

    0
    2021-09-12T21:38:30+00:00

    Answer:

    4.85%

    Step-by-step explanation:

    1450000 = 350000(x³⁰)

    x³⁰ = 4.1428571429

    30lgx = lg4.1428571429

    lgx = 0.0205766653

    x = 10^0.0205766653

    x = 1.0485198708

    104.85%

    So, interest is 4.85%

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