9600 dollars is placed in an account with an annual interest rate of 5%. To the nearest year, how long will it take for the account value to

Question

9600 dollars is placed in an account with an annual interest rate of 5%. To the nearest year, how long will it take for the account value to reach 37800 dollars?

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Arianna 1 month 2021-10-15T01:44:26+00:00 1 Answer 0 views 0

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    2021-10-15T01:46:22+00:00

    Answer: lt will take 28.09 years for the account value to reach $37800

    Step-by-step explanation:

    Hi, to answer this question we have to apply the compounded interest formula:

    A = P (1 + r) t

    Where:  

    A = Future value of investment (principal + interest)  

    P = Principal Amount  

    r = Annual Nominal Interest Rate (decimal form)

    Replacing with the values given

    37800= 9600 (1+0.05)^t

    Solving for t (years)

    37800/9600 = 1.05^t

    3.9375 = 1.05^t

    log 3.9375 = log 1.05^t

    log 3.9375 = t (log 1.05)

    log 3.9375/log 1.05 = t

    t = 28.09 years

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