Question

Your older sister deposited $5,000 today at 7 percent interest for 5 years. You would like to have just as much money at the end of the next 5 years as your sister will have. However, you can only earn 5.75 percent interest. How much more money must you deposit today than your sister did if you are to have the same amount at the end of the 5 years?

Answer 1

At 7% rate:

FV = PV (1 + rate) ^ year

      = 5,000 (1 + 0.07) ^ 5

      = 5,000 × 1.07 ^ 5

      = 5,000 × 1.40255

      = 7,012.75

At 5.75% rate:

As per the condition given,

FV = PV (1 + rate) ^ year

7,012.75 = PV (1 + 0.0575) ^ 5

7,012.75 = PV × 1.0575 ^ 5

7,012.75 = PV × 1.322518

7,012.75 / 1.322518 = PV

PV = 5,302.57

Amount of more money = PV at 5.75% rate – PV at 7% rate

                                        = 5,302.57 – 5,000

                                         = 302.57 (Answer)