Discounted Loans

[Happydesta]

Here is my problem:
David obtained a $500,000 discounted housing loan at 7.58% interest rate for 15 years.
Calculate
a. The actual amount he received
b. The effective interest rate on the discounted loan.

P=dl-dl*r*t
P=500,000-(500,000*.0758*15)
P= 68,500

rs= r/1-r*t
rs=.0758/1-.0758*15
rs=.55

reff=(1+r/m)^m-1
reff=(1+.55/1)^1-1
reff=.55

Is this correct? It seems like the interest rate is really high. The discounted loans confuse me.

 

[tkhunny]

1) You really have not specified sufficient information for an appropriate solution to be obtained.
2) Your first calculation exposes the problem. Whatever that is, your adjustment is greater than your principle. You should have gotten a negative value! Obviously, you didn't like that, either, so you wote a positive number instead. That doesn't work.
3) See Note #1. Is this loan a repayment of the entire 500,000 in a single lump at the end of the 15 years?
4) The interest rate can be rather high.

\(\displaystyle 500,000*1.0758^{-15}\;=\;167,107.87\)

500,000 - 167,107.87 = 332,892.13 in interest over the 15 years. That may be only 2/3 of the 500,000, but it is 200% when compared to 167,107.87.

Figure out how to expose the entire problem, them maybe we can talk.

 

[Happydesta]

The question that I posted is the entire question in my homework. I missed a class due to illness and am now trying to make it up. Part of this is my lack of understanding of what a discounted loan actually is. Is it correct that 68,500 is the actual loan amount or is that the upfront charge of interest and the remainder is the loan amount?

Ok so thinking about it. The amount of the loan he recieved is 431500. So then the interest is charged on that amount.

 

[tkhunny]

Since I already discarded your previous answer as obviously incorrect, I really don't know how to respond to additional questions about it. 68500 is nothing. Throw it out.

You have not specified the entire problem. Perhaps you have included what it says in the problem statement, but there remains missing information. Maybe it's in the section heading or the just-prior readings. Where did your get your formulas? There is more information than you have provided.