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20 April, 11:19

Find the accumulated value of an investment $10,000 for 3 years at an interest of 7% if the money is compounded semiannually; compounded quarterly; compounded monthly; compounded continuously

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  1. 20 April, 13:45
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    Correct answer: 1) AV = 12,290 $, 2) AV = 12,310 $, 3) AV = 12,330 $,

    4) AV = 12,337 $

    Step-by-step explanation:

    Given:

    I = 10,000$

    n = 3 years

    p = 7% = 0.07

    Accumulated value of an investment is calculated with next formula:

    AV = I · (1 + (p/a)) ᵃⁿ where is:

    AV - accumulated value

    I - investment

    p - interest

    a - number of calculation parts during one year as the accounting period

    n - number of years as the accounting period

    1) money is compounded semiannually

    a = 2 and a · n = 2 · 3 = 6

    AV = I · (1 + (p/a)) ᵃⁿ = 10,000 · (1 + (0.07/2)) ⁶ = 10,000 · 1.229 = 12,290 $

    AV = 12,290 $

    2) money is compounded quarterly

    a = 4 and a · n = 4 · 3 = 12

    AV = I · (1 + (p/a)) ᵃⁿ = 10,000 · (1 + (0.07/4)) ¹² = 10,000 · 1.231 = 12,310 $

    AV = 12,310 $

    3) money is compounded monthly

    a = 12 and a · n = 12 · 3 = 36

    AV = I · (1 + (p/a)) ᵃⁿ = 10,000 · (1 + (0.07/12)) ³⁶ = 10,000 · 1.233 = 12,330 $

    AV = 12,330 $

    4) money is compounded continuously

    Accumulated value of an investment continuously compounded is calculated with next formula:

    AV = I · eⁿᵇ where is:

    n - number of years as the accounting period

    b = p = 7% = 0.07

    n · b = 3 · 0.07 = 0.21

    AV = 10,000 e⁰²¹ = 10,000 2.7183⁰²¹ = 10,000 1.2337 = 12,337 $

    AV = 12,337 $

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