Question

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?

Answer 1

$3753.64

Explanation:

Initial amount = $3600

Interest rate = 3.52%

n = 1 (once in a year)

Time = 1 years

No of years = 2

Compound interest

A =
`P(1 + (r)/(n) )^n*t`

• A = 3600(1 + 0.352/1) ^1*1

= $3726.72

• Interest earned = 3726.72 - 3600

= $126.72

• Tax = 40% of the interest earned

=
`(40)/(100)*126.72` = $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 =
`P(1 + (r)/(n) )^n*t`

• A = 3676( 1+0.0352/1)^1*1

= 3676(1.0352)

= $3805.4

• Interest earned = 3805.4 - 3676

= $129.4

• Tax =
  `(40)/(100)*129.4`

= $51.76

• Net interest earned =129.4 - 51.76

= $77.64

• Net balance after 2nd year = 3676+ 77.64

= $3753.64