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27 September, 02:53

Marco wants to invest his savings in a bank for 3 years. He has borrowed £15,0000 to invest and receives offers from two banks. Bank 1 is: - 2.5 % per year compound interest and Bank 2 is: - 3.8% for 1st year and 1% for each extra year compound interest. Which bank should Marco choose to get the most interest over the 3 year period?

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  1. 27 September, 03:53
    0
    Marco should choose the first bank to get the most interest over 3 years (£1153.36)

    Step-by-step explanation:

    According to the question, Marco is trying to invest his savings of £15,000 in a bank for three (3) years.

    Two banks presented an offer with different interest rates. Bank 1 offers 2.5% interes rate per year while Bank 2 offers 3.8% interest rate for the 1st year and 1% interest rate for subsequent years.

    In order to calculate the interest amount offered by both banks, we use the formula:

    I = P * R * T : 100

    Where P = Principal amount to be invested

    R = interest rate

    T = Time in years

    I = Interest amount

    We will calculate the interest amount for each year, hence, T is 1 for each year.

    Bank 1:

    For 1st year;

    P = £15,000, R = 2.5%, T=1

    I = 15000 * 2.5 * 1 : 100

    I = 375

    To get the principal amount for year 2, we add 15000 + 375 = 15375

    2nd year;

    P = £15,375, R = 2.5%, T=1

    I = 15375 * 2.5 * 1 : 100

    I = 384.375

    Principal amount for year3 = 15375 + 384.375 = 15759.38

    3rd year;

    P = £15,759.38, R = 2.5%, T=1

    I = 15759.38 * 2.5 * 1 : 100

    I = 393.98

    Amount for three years = 15759.38 + 393.98 = £16153.36

    Hence, for the first bank, a total amount of £16153.36 was realized after three years with a total interest amount of £16153.36 - £15000 = £1153.36

    Bank 2:

    For 1st year;

    P = £15,000, R = 3.8%, T=1

    I = 15000 * 3.8 * 1 : 100

    I = 570

    To get the principal amount for year 2, we add 15000 + 570 = 15570

    N. B: The interest rate has been reduced for following years

    2nd year;

    P = £15,570, R = 1%, T=1

    I = 15570 * 1 * 1 : 100

    I = 155.7

    Principal amount for year3 = 15570 + 155.7 = 15725.7

    3rd year;

    P = £15,725.7, R = 1%, T=1

    I = 15725.7 * 1 * 1 : 100

    I = 157.257

    Amount for three years = 15725.7 + 157.257 = £15882.95

    Hence, for the second bank, a total amount of £15,882.95 was realized after three years with a total interest amount of £15882.95 - £15000 = £882.95

    The interest amount of Bank 1 (£1153.36) after three years of investing £15000 will be more than the interest amount (£882.95) of Bank2 after investing the same amount for 3 years. Hence, Marco should choose Bank 1 to invest his savings.
  2. 27 September, 06:43
    0
    Marcos Should invest with the first bank

    Step-by-step explanation:

    Formula for finding compound interest is: A = p (1+/frac{r}{n}) ^{nt}

    where

    A = the future value of the investment

    P = the principal investment amount (the initial deposit)

    r = the annual interest rate (decimal)

    n = the number of times that interest is compounded per unit t

    t = the time the money is invested

    If marcos choose to invest with the first bank

    A = 15000 (1+/frac{0.025}{12}) ^{12*3} = £16166.81

    If he choose to invest with the second bank

    His principal become 15570 in the first year because of the 3.8% offer from the bank and t becomes 2.

    A = 15570 (1+/frac{0.01}{12}) ^{12*2} = £15884.27

    Comparing the future value of his investment from both bank, Marcos will get more interest from investing with the first bank.
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