Question

You have been saving to buy a house. The total cost will be $10 million. You currently have about $2.3 million. If you earn 5% on your money.

(i)how long will you have to wait until you are able to buy the house?

(ii) At 16% how long will you have to wait?

Answer 1

1) Present value = Future value * 1 / (1+interest)^{number of years}

   2300000 = 10000000 *  1 / (1+0.05)^{number of years}

     2300000 = 10000000 *  1 / (1.05)^{number of years}

     2300000 /10000000 = 1 / (1.05)^{number of years}

   0.23 = 1 / (1.05)^{number of years}

   (1.05)^{number of years} = 1/0.23

   (1.05)^{number of years} = 4.35

   (1.05)^{number of years} = (1.05)^30.12

   number of years = 30.12 years

2) Present value = Future value * 1 / (1+interest)^{number of years}

      2300000 = 10000000 *  1 / (1+0.16)^{number of years}

     2300000 = 10000000 *  1 / (1.16)^{number of years}

     2300000 / 10000000 = 1 / (1.16)^{number of years}

   0.23 = 1 / (1.16)^{number of years}

   (1.16)^{number of years} = 1/0.23

   (1.16)^{number of years} = 4.35

   (1.16)^{number of years} = (1.16)^9.9

   number of years  = 9.9 years