Math

Can anybody show me step by step pls?
A man invests $3000 in an account that pays 7.5% interest per year, compounded quarterly.
1. Find the amount after 3 years? (Round your answer to the nearest cent.)
how much $?

2. How long will it take for the investment to double? (Round your answer to two decimal places.)
how many yrs?

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  1. i = .075/4 = .01875

    1. n = 4(3) = 12
    amount = 3000(1.01875)^12 = 3749.15

    2.

    3000(1.01875)^n = 6000 , where n is the number of quarter years
    1.01875^n = 2
    take logs of both sides and use use of logs
    n log 1.01875 = log 2
    n = log 2/log 1.01875 = appr 37.313
    = 37.313../4 or appr 9.3 years

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  2. so just to clarify the answer is 37.313 or 9.3? if i was to round to two decimal places

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  3. It should be clear to you that the 37.313 is the number of quarter years, and if I divide that by 4
    I would get years

    37.313../4 = 9.33 years rounded to 2 decimal places

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