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25 November, 08:01

Determine the amount of money in a savings account at the end of 3 years, given an initial deposit of $9,000 and an annual interest rate of 4 percent when interest is compounded:

Use Appendix Afor an approximate answer, but calculate your final answer using the formula and financial calculator methods. (Do not round intermediate calculations. Round your final answers to 2 decimal places.) Future value:

a. Annually

b. Semiannually

c. Quarterly

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  1. 25 November, 10:13
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    The correct answer for option (a) is $10,124, option (b) is $10,135 and option (c) is $10,141.

    Explanation:

    According to the scenario, the given data are as follows:

    Initial amount (p) = $9,000

    Annual interest rate (r1) = 4%

    Semi annual interest rate (r2) = 4% / 2 = 2%

    Quarterly interest rate (r3) = 4% / 4 = 1%

    Time period (annual) (n1) = 3 years = 3

    Time period (semi-annual) (n2) = 3 * 2 = 6

    Time period (quarterly) (n3) = 3 * 4 = 12

    So, we can calculate future value by using following formula:

    A = P (1 + r) ^n

    (a). Putting the value in the formula

    A = P (1 + r1) ^n1

    = $9,000 (1 + 4%) ^3

    = $9,000 x (1.04) ^3

    = $10,124

    (b). Putting the value in the formula

    A = P (1 + r2) ^n2

    = $9,000 (1 + 2%) ^6

    = $9,000 x (1.02) ^6

    = $10,135

    (c.) Putting the value in the formula

    A = P (1 + r3) ^n3

    = $9,000 (1 + 1%) ^12

    = $9,000 x (1.01) ^12

    = $10,141
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