Suppose that you have $1,000 at hand that you can place in a bank gaining 5%...

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Suppose that you have $1,000 at hand that you can place in abank gaining 5% annually in interests; assume that this interestrate is your personal discount rate. Your friend asks you to lendhim $1,000 so he can buy a new gadget that he does not really need.He promises to pay back the full amount, plus interest, in acertain amount time. Assume that you really do not think that yourfriend should buy this new gadget, except, of course, if you wereto make a profit out of it.
(a) Your friend offers to pay you back $1,006 in one year. Whatshould you do? Demonstrate how munch money you would make if youwere to place your $1,000 in the bank and compare it with theamount of money you would make if you were to accept your friend’soffer.
(b) Your friend offers to pay you back $1,060 in one year. Whatshould you do? Demonstrate.
(c) Your friend offers to pay you back $500 in one year, another$400 in two years and $200 in three years. What should you do?Demonstrate.
(d) Your friend offers to pay you back $200 in one year, another$400 in two years and $500 in three years. What should you do?Demonstrate.
(e) Suppose instead that your friend just saw a publicity forthis gadget he really does not need but really wants, and that thisgadget will come into the market in x years and will cost $1,000.Your friend is worried that he will spend his money on otheruseless gadgets before this one comes out, so he offers to pay you$y each year if you agree to give him $1,000 in xyears when thegadget gets on the market. Assume you can still earn 5% annualinterest by placing the money your friend gives you in a bank, andthat in x years you have to withdraw all of the money from thebank; assume again that this interest rate is your personaldiscount rate.
(i) If x = 1, that is, your friend pays you $y today, and youpay him back $1,000 in a year. For what amount of money y will yoube indifferent between accepting or refusing his offer?
(ii) If x = 5, for which amount of money y will you beindifferent between accepting or refusing his offer?
(iii) Suppose now that instead of giving you the money eachyear, your friend gives youonly $y today. If x = 10, for whichamount of money y will you be indifferent between accepting orrefusing your friend’s offer?

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4.1 Ratings (665 Votes)

a If i invest 1000 in bank at 5 for 1 year i would get 1050 after 1 yr but if i give the same amount to friend so i would recieve 1006 in 1 yr so i am better off with investing that amount in the Bank Bank Amount 1000 Rate 5 Time years 1 Compounding factor 105 Final Amount 1050 Note Compounding factor 1ratetime With Friend Final Amount 1006 b similarly in this case with Bank See Answer

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Suppose that you have $1,000 at hand that you can place in abank gaining 5% annually in interests; assume that this interestrate is your personal discount rate. Your friend asks you to lendhim $1,000 so he can buy a new gadget that he does not really need.He promises to pay back the full amount, plus interest, in acertain amount time. Assume that you really do not think that yourfriend should buy this new gadget, except, of course, if you wereto make a profit out of it.(a) Your friend offers to pay you back $1,006 in one year. Whatshould you do? Demonstrate how munch money you would make if youwere to place your $1,000 in the bank and compare it with theamount of money you would make if you were to accept your friend’soffer.(b) Your friend offers to pay you back $1,060 in one year. Whatshould you do? Demonstrate.(c) Your friend offers to pay you back $500 in one year, another$400 in two years and $200 in three years. What should you do?Demonstrate.(d) Your friend offers to pay you back $200 in one year, another$400 in two years and $500 in three years. What should you do?Demonstrate.(e) Suppose instead that your friend just saw a publicity forthis gadget he really does not need but really wants, and that thisgadget will come into the market in x years and will cost $1,000.Your friend is worried that he will spend his money on otheruseless gadgets before this one comes out, so he offers to pay you$y each year if you agree to give him $1,000 in xyears when thegadget gets on the market. Assume you can still earn 5% annualinterest by placing the money your friend gives you in a bank, andthat in x years you have to withdraw all of the money from thebank; assume again that this interest rate is your personaldiscount rate.(i) If x = 1, that is, your friend pays you $y today, and youpay him back $1,000 in a year. For what amount of money y will yoube indifferent between accepting or refusing his offer?(ii) If x = 5, for which amount of money y will you beindifferent between accepting or refusing his offer?(iii) Suppose now that instead of giving you the money eachyear, your friend gives youonly $y today. If x = 10, for whichamount of money y will you be indifferent between accepting orrefusing your friend’s offer?