Question

Your older sister deposited $2,000 today at 6.5 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 6 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? $32.19 $47.62 $38.78 $40.21 $53.39

Answer 1

The future balances will increase to (initial balance) x ( (1 + interest rate) ^ (# of years compounded) ) For your older sister, this is 2000 x ( 1.065 ^ 5), where ^ means 'raised to the power'. For you this is B x ( 1.06 ^ 5) At end of 5 years, sister has $2000 x 1.037 = $2740.17 you have B x 1.33823. So, in order to end up with the same balance as sister, B x 1.33823 must = $2740.17, or B = $2740.17 / 1.33823 B = 2047.62 must be your approximate initial balance. So, the answer is $47.62 is how much more money must you deposit today.