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Laura invests $3600 in a savings account for 2 years. The account pays 3.52% compound interest per annum. Laura has to pay 40% tax on the interest earned each year. The tax is taken from the account at the end of each year. How much is in the account at the end of 2 years?

Respuesta :

Answer:

$3753.64

Step-by-step explanation:

Initial amount = $3600

Interest rate = 3.52%

n = 1 (once in a year)

Time = 1 years

No of years = 2

Compound interest

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

  • A = 3600(1 + 0.352/1) ^1*1

   = $3726.72

  • Interest earned = 3726.72 - 3600

                          =  $126.72

  • Tax = 40% of the interest earned

       = [tex]\frac{40}{100}*126.72[/tex]   = $50.69 (This amount is deducted from interest )

  • Net interest earned after 1 year = 126.72 - 50.69

                                                     = $76

  • Balance after 1 year = $3600 + $76

                                  = $3676

Similarly for the 2nd year

Compound interest

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

  •     A = 3676( 1+0.0352/1)^1*1

         = 3676(1.0352)

           =  $3805.4

  • Interest earned = 3805.4 - 3676

                           = $129.4

  • Tax = [tex]\frac{40}{100}*129.4[/tex]

       = $51.76

  • Net interest earned =129.4 - 51.76

                                 = $77.64

  • Net balance after 2nd year  = 3676+ 77.64

                                               = $3753.64

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