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17 May, 03:24

Suppose Jennifer deposits $500 in an account at the end of this year, $400 at the end of the next year, and $300 at the end of the followin g year. If her opportunity cost rate is 7.5 percent, how much will be in the account immediately after the third deposit is made? How m uch will be in the account at the end of three years if t he deposits are made at the beginning of each year?

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  1. 17 May, 03:46
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    Formula required to find remaining amount in account:

    A = P (1 + r / 100) ^n

    Here

    A represents future value

    P represents present value

    r represents rate of interest

    n represents time period.

    a)

    As Jennifer deposits $500 in an account at the end of this year, $400 at the end of the next year, and $300 at the end of the following year.

    Therefore by putting the values in the above formula, we get

    At the end of 3 years:

    A = 500 * (1 + 7.5 / 100) ^2

    A = 500 * (1.075) ^2

    At the end of next year:

    A = 400 * (1 + 7.5 / 100)

    A = 400 * (1.075)

    At the end of following year:

    A = 300

    Adding all these together, we get

    A = 500 * (1.075) ^2 + 400 * (1.075) + 300

    A = $1307.8125

    b)

    At the end of 3 years:

    A = 500 * (1 + 7.5 / 100) ^3

    A = 500 * (1.075) ^3

    At the end of next year:

    A = 400 * (1 + 7.5 / 100) ^2

    A = 400 * (1.075) ^2

    At the end of following year:

    A = 300 * (1.075)

    Adding all these together, we get

    A = 500 * (1.075) ^3+400 * (1.075) ^2+300 * (1.075)

    A = $1405.90
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