Equivalent payments

[elisabeth63]

During a 50/50 sale a furniture store will sell its merchandise for 50% down with the balance payable in 6 mos. No interest is charged for the first 6 mos. What 100% cash price should the store accept on a $1845 suite if they can earn a rate of return of 10.75% on its funds?

Okay, I've calculated the price they would receive on the 50/50 deal
922.50 + 922.50 (.1075) (6/12)= 972.08 922.50+972.08=1894.58

but I don't know how you go about figuring out what 100% cash price they should accept. My prof. doesn't teach and my textbook is of no help.
Can someone explain to me how you go about solving this?

 

[Denis]

During a 50/50 sale a furniture store will sell its merchandise for 50% down with the balance payable in 6 mos. No interest is charged for the first 6 mos. What 100% cash price should the store accept on a $1845 suite if they can earn a rate of return of 10.75% on its funds?

Okay, I've calculated the price they would receive on the 50/50 deal
922.50 + 922.50 (.1075) (6/12)= 972.08 922.50+972.08=1894.58

but I don't know how you go about figuring out what 100% cash price they should accept. My prof. doesn't teach and my textbook is of no help.
Can someone explain to me how you go about solving this?

Why don't you get the prof. fired then? :shock:

Your 972.08 is correct as value of 922.50 in 6 months, but is not required here.

You need to discount (which means find present value) of the 922.50 due in 6 months;
that's done this way: 922.50 / (1 + .1075 / 2) = 875.44

So cash price = 922.50 + 875.44

I've assumed 10.75% means annual rate compounded semi-annually.

 

[elisabeth63]

Denis,
Thanks for the help. I think I get it now.