Mark Johnson saves a fixed percentage of his salary at the end of each year. This year he saved $2,000. 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 $2,000 plus five more. If the investments earn a return of 13% per year, how much will Mark have at the end of six years?

The correct answer is:

$17,437.28

Explanation:

First of all, let us lay out the particulars that will aid us in our calculations:

Amount saved in year 1 = $2000

Number of years saved in total = 6 years

annual rate of savings increase = 10% increase on the amount for that year to the next year

Annual return on investment = 13%.

Next, let us calculate the 10% increase in savings from years 2 to 6.

Year 1 investment = $ 2000

Year 2 investment = Year 1 saving + 10% of year one saving

hence, investment 2 saving = 2000 + (10/100 × 2000) = 2000 + (0.1 × 2000)

Year 2 investment = 2000 +200 = $2,200.

Year 3 investment = year 2 saving + (0.1 × year 2 saving) = 2200 + (0.1 × 2200)

year 3 investment = 2200 + 220 = $2,420

Year 4 investment = 2420 + (0.1 × 2420) = 2420 + 242 = $2,662

Year 5 investment = 2662 + (0.1 × 2662) = 2662 + 266.2 = $2928.2

Year 6 investment = 2928.2 + (0.1 × 2928.2) = 2928.2 + 292.82 = $3,221.02

Next, let us create a table to show the total amount for each year.

Note, to determine the 13% annual investment return on each year:

13% = 13/100 = 0.13. So, we will multiply the investment for each year with 0.13 to get the annual investment. It is shown hence:

Year   Investment (I) ($)   Annual return (AR) ($)    Total amount (I + AR) ($)

1             2000                   260                                     2260

2            2200                   286                                     2486

3            2420                   314.6                                   2734.6

4            2662                   346.06                               3008.06

5            2928.2                380.67                               3308.87

6            3221.02               418.73                                3639.75

Total                                                                             17,437.28    

Therefore, at the end of 6 years mark would have $17,437.28 (approx. $17,437)

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