Mathematics

Question

Anastasia was trying to decide which investment plan would be best over 10 years. Bank A was offering 8.5% simple interest on her money using the formula I=Prt Bank B was offering 8% compounded annually using the formula A=P(1+r)^t. Which bank is a better investment if she has $2,000 to invest for 10 years?


A. Bank A is the better investment. In 10 years, her $2,000 will grow to $4,317.85, and with bank B, her $2,000 will grow to $3,700.

B. Bank B is the better investment. In 10 years, her $2,000 will grow to $4,317.85, and with bank A, her $2,000 will grow to $3,600.

C. Bank A is the better investment. In 10 years, her $2,000 will grow to $4,521.97, and with bank A, her $2,000 will grow to $3,700.

D. Bank B is the better investment. In 10 years, her $2,000 will grow to $4,317.85, and with bank A, her $2,000 will grow to $3,700.

2 Answer

  • A
    2,000×(1+0.085×10)
    =3,700
    B
    2,000×(1+0.08)^(10)
    =4,317.85
    Bank B is the better investment. In 10 years, her $2,000 will grow to $4,317.85, and with bank A, her $2,000 will grow to $3,700
  • Bank A is the better investment. In 10 years, her $2,000 will grow to $4,317.85, and with bank B, her $2,000 will grow to $3,700.

    What is simple interest?

    Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time.

    Simple interest = [tex]\frac{Principal * Rate * Time}{100}[/tex]

    What is compound interest?

    Compound interest is an interest accumulated on the principal and interest together over a given time period. The interest accumulated on a principal over a period of time is also accounted under the principal.

    [tex]A = P (1+\frac{r}{100} )^{t}[/tex]

    where,

    A = final amount

    P = initial amount

    r = rate per annum

    t = time in years

    According to the question

    Anastasia was trying to decide which investment plan would be best over 10 years  

    Bank A:

    Simple interest

    Principal = $2,000

    Rate per annum  = 8.5%

    Time in years = 10 years

    Now , using simple interest formula

    Simple interest = [tex]\frac{Principal * Rate * Time}{100}[/tex]

    Simple interest = [tex]\frac{ 2000 * 8.5 * 10 }{100}[/tex]

                              = 1700

    Total Amount after 10 years   =   $2,000 +  $ 1700

                                                    =   $3700

    Bank B:

    Compound Interest

    Rate per annum = 8%

    Time in years = 10

    Principal =  $2,000

    Now,

    Applying compound interest formula

    [tex]A = P (1+\frac{r}{100} )^{t}[/tex]

    [tex]A = 2000 (1+\frac{8}{100} )^{10}[/tex]

    [tex]A = 2000 (1.08} )^{10}[/tex]

    A = 4,317.85

    Hence, Bank A is the better investment. In 10 years, her $2,000 will grow to $4,317.85, and with bank B, her $2,000 will grow to $3,700.

    To know more about compound interest and simple interest here:

    https://brainly.com/question/22621039

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