Question

1) Solve.

Answer 1

Step-by-step explanation:

1. Given : P = $1200 , R = 5%, T = 7 years

   Therefore, the simple interest is, $SI = \frac{PTR}{100}$

                                                                $=\frac{1200 \times 7 \times 5}{100}$

                                                                 = $ 420

   Therefore, total amount Manny will have is A = P + Si

                                                                                = 1200 +420

                                                                                = $ 1620

2. Given : P = $1200 , r = 5%, t = 7 years, n = 12 times (compounded)

   So the amount is :

  $A=P\left(1+\frac{r}{n}\right)^{nt}$

  $A=1200\left(1+\frac{0.05}{12}\right)^{12\times 7}$

      = 1692.17

  So Manny would have approximately $ 1692 when compounded monthly.

3. Given :

  The amount of stock = $ 100

   rate of depreciation = 3%

    Time = 20 years.

    Therefore, using compound interest, we get

    Future value = initial value x $(1-\text{rate})^{number of years}$

                          = $100 \times (1 - 3 \%)^{20}$

                          = 54.38

  So after 20 years, the value would be $ 54.38

4. Given :

  Initial amount, i = 40 gram

  time, t = 40 days

  half life of the isotope, h = 8 days

  1/2 is used because of half life

  Therefore, the final amount is given by :

  $a=i \times \left(\frac{1}{2}\right)^{t/h}$

  $a=40\times \left(\frac{1}{2}\right)^{40/8}$

    = 1.25 gram

 So after 40 days, 1.25 gram will be left.

5. Let  p =  pizza and d = drink

   So according to the question,

    2p + 4d = $ 15 ....(i)

    4p + 7d = $ 30...(ii)

   Equation equation (i) and (ii), we get

   d = $0

   and p = $ 7.5