Jessie Jones believes her hair salon is worth 20000 and esti

Jessie Jones believes her hair salon is worth $20,000 and estimates that its value will grow at 10% per year compounded annually for the next 3 years. If she sells the business, the funds will be invested at 8% compounded quarterly. (a) Find the future value if she holds onto the business. (b) What price should she insist on now if she sells the business?

Solution

P =20,000 $

i(s) = 10%

i(b,q) = 8%

so i yearly

i(b) = (1.08)^4 -1 = 36.04%

F(s) = P*[(1+i)^n-1]/[i*(1+i)^n]

F(s) = 20,000 * [ 1.1^3]

F(s) = 26,620 $

F(b) = 20,000 * [1.36^3]

F(b) = 50,309 $

So difference = 50,309 - 26620 = 23,689 $

to have 50,309 $ after 3 years at 10% annually

P = F/(1+i)^n

P = 50309 / 1.1^3

P = 37,798 $