Question

A friend asks to borrow $ 50 from you and in return will pay you $ 53 in one year. If your bank is offering a 5.7 % interest rate on deposits and​ loans: a. How much would you have in one year if you deposited the $ 50 ​instead? b. How much money could you borrow today if you pay the bank $ 53 in one​ year? c. Should you loan the money to your friend or deposit it in the​ bank?

Answer 1

Answer:

52.85 / 50.14 / yes

Explanation:

the key to answer this question is to understand the logic of present values / future values:

$FV=PV*(1+i)^{n}$

$PV=FV*(1+i)^{-n}$

where FV is future value, PV is the present value, i is the periodic interest rate and n is the number of periods. So applying to this particular problem we have:

a. if we deposit today 50, we are been asked to calculate the future value, so:

$FV=50*(1+0.057)^{1}$

$FV=52.85$

b.if we want to have 53 in one year, we are been asked to calculate a present value:

$PV=53*(1+0.057)^{-1}$

$PV=50.14$

c. is clear that is better to borrow to the friend because in one year he will pay more than bank