Question

Your older sister has deposited $5,000 today at 8.5 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 7 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.

a. $321

b. $360

c. $387

d. $401

e. $413

Answer 1

Amount deposited by your sister today for 5 years= $5000

Calculating its Future value at year end 5:-

Future Value = Invested Amount*(1+r)^n

Where,

r = Interest rate = 8.5%

n= no of periods = 5 years

Future Value = $5,000*(1+0.085)^5

Future Value = $5000*1.50365669018

Future Value = $7,518.28

So, the amount your sister will have in year end 5 is $7518.28

- Since you too wanted to have the same Future value at year end 5 but can only earn interest of 7%

Calculating the amount you need to deposit today:-

Present Value = Future Value /(1+r)^n

Where,

r = Interest rate = 7%

n= no of periods = 5 years

Present Value = $7518.28/(1+0.07)^5

Present Value = $7518.28/1.4025517307

Present Value = $5360.43

Amount you need to depsoit today is $5360.43

- the 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 = $5360.43 - $5000

= $360.43

Option B

If you need any clarification, you can ask in comments.    

If you like my answer, then please up-vote as it will be motivating