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7 November, 09:05

Mark Johnson saves a fixed percentage of his salary at the end of each year. This year he saved $2,500. For each of the next 5 years, he expects his salary to increase at an 10% annual rate, and he plans to increase his savings at the same 10% rate. There will be a total of 6 investments, the initial $2,500 plus five more. If the investments earn a return of 13% per year, how much will Mark have at the end of six years

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  1. 7 November, 12:50
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    Mark will have at the end of six years the amount of $25,865.74

    Explanation:

    According to the given data we have the following:

    First investment = 2500

    Investment increasing at rate of 10%

    Interest rate = 13%

    t=6 years

    Present value is given by formula = C * [ ((1+g) ^n / (1+i) ^n) - 1 ] / (g-i)

    C is first value = 2,500

    g is increase in investment = 0.10

    i is intrest rate = 0.13

    n is no of years = 6

    Putting values into the equation

    P = 2500 * [ ((1 + 0.10) ^6 / (1+0.13) ^6) - 1 ] / (0.10-0.13) 1.771561 2.08195

    P = 2500 * [ ((1.10) ^6 / (1.13) ^6) - 1 ] / (-0.03)

    P = 2500 * [0.8509142870866 - 1 ] / (-0.03)

    P = 2500 * (-0.14908571) / (-0.03)

    P = 2500 * 4.9695236

    P=$12,423.809

    Future value = P * (1+i) ^t

    = $12,423.809 * (1+0.13) ^6

    = $25,865.74

    Mark will have at the end of six years the amount of $25,865.74
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