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23 December, 10:34

To fund your dream around-the-world vacation, you plan to save $1,175 per year for the next 15 years starting one year from now. If you can earn an interest rate of 5.53 percent, how much will you have saved for your vacation

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  1. 23 December, 10:59
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    I will save $26,390

    Explanation:

    A fix Payment for a specified period of time is called annuity. The Compounding of these payment on a specified rate is known as Future value of annuity. In this question $1,175 per year payment for 15 years at 5.53% interest rate is also an annuity.

    We can calculate the amount of saving by calculating the future value of the given annuity.

    Formula for Future value of annuity is as follow

    Future value of annuity = FV = P x ([ 1 + r ]^n - 1) / r

    Where

    P = Annual payment = $1,175

    r = rate of return = 5.53%

    n = number of years = 15 years

    Placing Value in the formula

    Future value of annuity = FV = 1,175 x ([ 1 + 5.53% ]^15 - 1) / 5.53%

    Future value of annuity = FV = 1,175 x ([ 1 + 0.0553 ]^15 - 1) / 0.0553

    Future value of annuity = FV = $26,390
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