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2 April, 17:21

You plan to invest some money in a bank account. Which of the following banks provides you with the highest effective rate of interest? a. Bank 1; 6.1% with annual compounding. b. Bank 2; 6.0% with monthly compounding. c. Bank 3; 6.0% with annual compounding. d. Bank 4; 6.0% with quarterly compounding. e. Bank 5; 6.0% with daily (365-day) compounding.

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  1. 2 April, 17:26
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    Option (d), Bank 4 offers the highest amount after a year

    Explanation:

    The total amount from each of the interest rates can be expressed as;

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

    where;

    A=Future value of investment

    P=Initial value of investment

    r=Annual interest rate

    n=Number of times the interest is compounded annually

    t=number of years of the investment

    a). Bank 1

    P=x

    r=6.1%=6.1/100=0.061

    n=1

    t=assume number of years=1

    replacing;

    A=x (1+0.061/1) ^ (1*1)

    A=x (1.061)

    A=1.061 x

    b). Bank 2

    P=x

    r=6%=6/100=0.06

    n=12

    t=1

    Replacing;

    A=x (1+0.06/12) ^ (12*1)

    A=x (1.005) ^12

    A=1.0617 x

    c). Bank 3

    P=x

    r=6%=6/100=0.06

    n=1

    t=1

    Replacing;

    A=x (1+0.06/1) ^ (1)

    A=1.0600 x

    d). Bank 4

    P=x

    r=6%=6/100=0.06

    n=4

    t=1

    A=x (1+0.06/4) ^ (4*1)

    A=x (1+0.015) ^4

    A=x (1.061)

    A=1.0614 x

    e). Bank 5

    P=x

    r=6%=6/100=0.06

    n=365

    t=1

    A=x (1+0.06/365) ^ (365*1)

    A=1.0618

    Option (d), Bank 4 offers the highest amount after a year
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