Interest portion on loans

CFA Level I Quant
#1

I had a conversation with my Uncle about taking a student loan vs. interest-free loan. Let’s say that I need $100K today for my expenses, at 3.5% annual rate for 10 years with payments due at the end of the year. Plugging in this value, I get $12,024 annual payments. Now, as an alternative, my Uncle is willing to offer me interest-free loan for 10 years. So, Interest payments would be $10K per year. However, if I have to calculate how much “extra” money I would give to the bank in terms of interest expense, I used a risk-free savings rate of 1%. i.e.

N = 10

PMT = 12024-10K = 2024

I/Y = 1

FV = 0

PV = ?

This gives me $19171. Is this a correct method to calculate the present value of the interest?

However, if I use I/Y = 3.5%, I get PV = 16,832. So, I am a little confused–is the penalty equal to 16832 or 19171? My uncle says it’s $19171 because his loan is risk-free. I believe both the numbers are wrong because I can take the loan and invest it at risk-free rate, reducing my effective interest rate. So, I would plug in I/Y = 3.5% - 1% = 2.5% which gives me PV = 17714.

Who is correct? I’d appreciate any thoughts.

#2

I think that you meant that the loan payments to your uncle would be $10,000 per year; they’re all principal, no interest.

As for the discount rate, I’ll have to ponder that one for a bit.

#3

Yes, I meant that loan payments would be $10K per year to my Uncle and no interest will be included. I look forward to hearing from you about discount rates.

#4

Bumping this…