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25 April, 21:08

Damon is saving up money for a down payment on a condominium. He currently has $4818$ 4818, but knows he can get a loan at a lower interest rate if he can put down $5381$ 5381. If he invests the $4818$ 4818 in an account that earns 5.6%5.6% annually, compounded continuously, how long will it take Damon to accumulate the $5381$ 5381? Round your answer to two decimal places, if necessary.

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  1. 26 April, 00:30
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    Time t = 2.03 years

    Step-by-step explanation:

    The standard formula for compound interest is given as;

    A = P (1+r/n) ^ (nt) ... 1

    For n = 1

    A = P (1+r) ^ (t)

    Making t the subject of formula;

    t = ln (A/P) : ln (1+r) ... 2

    Where;

    A = final amount/value

    P = initial amount/value (principal)

    r = rate yearly

    n = number of times compounded yearly.

    t = time of investment in years

    For this case;

    A = $5381

    P = $4818

    t = ?

    n = 1

    r = 5.6% = 0.056

    Using equation 2;

    t = ln (5381/4818) : ln (1+0.056)

    t = 2.028243842925

    t = 2.03 years (to two decimal place)
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