Matthew invested $5000 in an account that earns 3.8% interest, compounded annually. The formula for compound interest is A(t) = P(1 + i)t.

Question

Matthew invested $5000 in an account that earns 3.8% interest, compounded annually. The formula for compound interest is A(t) = P(1 + i)t. How much did Matthew have in the account after 3 years?
A. $6900.00
B. $5594.37
C. $5570.00
D. $5591.93

0

Answers ( No )

    0
    2021-10-11T03:15:20+00:00

    Yup D Is Right Because if you divide by 3.8% * 5000 you get d

    0
    2021-10-11T03:15:31+00:00

    Answer:

    D. $5591.93.

    Step-by-step explanation:

    We have been given that Matthew invested $5000 in an account that earns 3.8% interest, compounded annually.

    We will use compound interest formula to solve our given problem.

    A=P(1+\frac{r}{n})^{nt}, where,

    A = Final amount after t years,

    P = Principal amount,

    r = Annual interest rate in decimal form,

    n = Number of times interest is compounded per year,

    t = Time in years.

    Let us convert our given interest rate in decimal form.

    3.8\%=\frac{3.8}{100}=0.038

    Upon substituting our given values in above formula we will get,

    A=\$5000(1+\frac{0.038}{1})^{1*3}

    A=\$5000(1+0.038)^{3}

    A=\$5000(1.038)^{3}

    A=\$5000*1.118386872

    A=\$5591.93436\approx \$5591.93

    Therefore, Matthew will have an amount of $5591.93 is his account after 3 years and option D is the correct choice.

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