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26 June, 04:14

Your dream is to buy a yacht currently valued at $300,000. You decide to put some money aside at the end of each month so you can buy your yacht without having to take out a loan. The bank guarantees an annual percentage rate of 5.1% as long as you have an account with them. If you decide to put aside $500 each month how long will it take you to buy this yacht if the current price stays the same? (Round fractional year up).

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  1. 26 June, 07:45
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    It will take you 79 years to buy the yacht

    Explanation:

    The future amount of an investment can be calculated using the formula;

    A=P (1+r) ^n

    where;

    A=Future value of the investment

    P=Initial deposit

    r=annual interest rate

    n=number of years of the investment

    In our case;

    A=300,000 since current price remains the same

    P = (500*12) = 6,000 yearly

    r=5.1%=5.1/100=0.051

    n=unknown

    replacing;

    300,000=6,000 (1+0.051) ^n

    6,000 (1.051) ^n=300,000

    1.051^n=300,000/6,000

    1.051^n=50

    ln 1.051^n=ln 50

    n ln 1.051=ln 50

    0.0497 n=3.912

    n=3.192/0.0497

    n=78.65 rounded up to 79 years

    It will take you 79 years to buy the yacht
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