Finance Question

[parade of idiots]

I am having a hard time with this problem.

John signed a $10000 note at Meridian Bank. The bank charges a 7% discount rate. Suppose the loan is for 150 days. Use the ordinary interest to find the (a) proceeds and (b) effective rate charged by the bank (rounded to the nearest tenth percent).

Any help is appreciated.

 

[parade of idiots]

10,000 @ 7% per year = 700 x 41.1% (150/365) = 287.67

(a) Proceeds = 10,000 - 287.67, or 9,712.33
(b) Effective rate: 287.67 / 9712.33 = 2.96% / 41.1% = 7.2%

this is what I keep getting.

 

[Ishuda]

I am having a hard time with this problem.

John signed a $10000 note at Meridian Bank. The bank charges a 7% discount rate. Suppose the loan is for 150 days. Use the ordinary interest to find the (a) proceeds and (b) effective rate charged by the bank (rounded to the nearest tenth percent).

Any help is appreciated.

You have the right idea but went abut it slightly wrong (as I understand the problem). Why did you add the 41.1% to the equation?

I haven't seen the term discount rate as I believe it is used here for a long time. A more common name (as I am understanding the question) is points (paid to the lender). So I will change the one sentence to "The bank charges 7 points and 0% interest for the loan" and hope I didn't change the problem.

7 points means 7% of the loan so the bank charges $700 (7% of $10000) for the loan and takes the $700 out of the loan amount. Thus
(a) proceeds = $10000 - $700 = $9300

Since you are being charged 0% interest on the loan, you just have to pay back the $10000 at the end of 150 days.

So, in effect, you borrowed $9300 and paid back the $9300 plus $700 interest in 150 days. Thus the interest, as a percent, was (700/9300) * 100 ~ 7.5269%. To convert this to a yearly rate we need to divide by 150 (to get a daily rate) and multiply by 365 (to get the yearly rate). Or, the effective interest rate i is
i = (700/9300) * 100 * (365/150)
~ 18.3154%

As a quick check on the reasonableness of the answer we note that 150 days is about one half year so the rate should be somewhere about twice 7% or somewhat above 14% and actually we didn't get to borrow the whole $10000 for that length of time so the interest rate is even higher again. 18% satisfies that reasoning, so we are at least close and, if we didn't make any mistakes, correct.

 

[jonah2.0]

I am having a hard time with this problem.

John signed a $10000 note at Meridian Bank. The bank charges a 7% discount rate. Suppose the loan is for 150 days. Use the ordinary interest to find the (a) proceeds and (b) effective rate charged by the bank (rounded to the nearest tenth percent).

Any help is appreciated.

Warning: Inebriated reveries ahead.

Alas Sir Denis, why didst thou allow this poor pilgrim go about wondering in the dark? Thou art ill perchance? Enchanted perchance?

'Tis clearly a simple discount problem.
Thus, we have the discounted value formula for the simple discount
P=S(1-dt)
where
P= principal/present value/discounted value/proceeds
S= amount or accumulated value
d= discount rate
t= time in years
By ordinary interest, surely this be but a reference to the Banker's rule. Google it up. Thus 150/360.

For the "effective rate", verily 'tis but a simple case of equating the simple interest present value formula with the simple discount present value formula and solving for the interest rate r.

Otherwise, stealing from Sir Denis, this could all just an imagination of my figment. Also, batteries sold separately.

I haven't seen the term discount rate as I believe it is used here for a long time. A more common name (as I am understanding the question) is points (paid to the lender). So I will change the one sentence to "The bank charges 7 points and 0% interest for the loan" and hope I didn't change the problem.

Definitely a good conjecture Sir Ishuda. As I recall however, points apply more on mortgage situations.

 

[Deleted member 4993]

sir (hic!) jonah, may yours truly enchant your perchance with this gem of simplicity:
5 mo. : 700
12 mo. : 700/5 * 12 = 1680 ; 1680/9300 = 18.06%

thassa way them discounters work: 30day months, 360day years.

[a far cry from canadian mortgages, where interest must effectively compound
semiannually, with an equivalent monthly rate to match payments which are
monthly, and that whole shebang declared appropriately to the borrower,
who usually doesn't give a sh*t anyway!]

let's have a look-see at the op's wording:
"john signed a $10000 note at meridian bank. The bank charges a 7% discount rate.
Suppose the loan is for 150 days."
means same as:
John borrowed $9300, arranged as a single payment loan of $10000 due in 5 months.

Why do teachers strive to confuse the issue?
Teacher to 5yr old johnny: What's 5 times 4?
Johnny, who doesn't know what "times" means: "dunno"
but ask johnny: If your dad gives you 5 bucks allowance per week
and owes you for 4 weeks...johnny will jump in at this point and
answer: 20 bucks, plus 2 bucks at 10% interest !!

apr?

 

[jonah2.0]

Let's have a look-see at the OP's wording:
"John signed a $10000 note at Meridian Bank. The bank charges a 7% discount rate.
Suppose the loan is for 150 days."
Means same as:
John borrowed $9300, arranged as a single payment loan of $10000 due in 5 months.

Nay Sir Denis, I say nay.
I say this be a textbook standard simple discount problem.
Requirement (a) stated so explicitly.
If this be not a simple discount problem, then why would requirement (b) ask for the effective rate (essentially, the equivalent simple interest rate that would result in the same present value or proceeds)?
Besides, I looked it up. At least one site here agree with my contention.
Examples from this site are virtual duplicates of OP.

Also, I very much doubt that someone who's totally lost on a simple accountng problem would be given a problem on "points".

 

[jonah2.0]

To keep it simple, all I was trying to say is that these 2 loans are identical:
1: discount 10000 by 7% leaving 9300 loan proceeds, single payment 10000 in 5 months
2: borrow 9300, and agree to repayment being a single payment of 10000 in 5 months

Methinks your trusty calculator is in need of new batteries.
10,000(1-.07*150/360) is not 9,300 by my calculator's reckoning.
Maybe I just drank too much beer again. With some anti allergy meds. Must be seeing things.
Better sleep it off. Can't keep eyes open.

 

[Ishuda]

Methinks your trusty calculator is in need of new batteries.
10,000(1-.07*150/360) is not 9,300 by my calculator's reckoning.
Maybe I just drank too much beer again. With some anti allergy meds. Must be seeing things.
Better sleep it off. Can't keep eyes open.

Ah yes, the old problem of answering what I think I read rather than answering what was really there.

 

[jonah2.0]

Of course it's not...who said it was?
Once more: both the lender and borrower have agreed on TOTAL INTEREST
of .07 * 10000 = 700. Over and out. Everybody seems to be missing my point.

My apologies Sir Denis if I somehow missed your point.
Unfortunately, your post of

To keep it simple, all I was trying to say is that these 2 loans are identical:
1: discount 10000 by 7% leaving 9300 loan proceeds, single payment 10000 in 5 months
2: borrow 9300, and agree to repayment being a single payment of 10000 in 5 months

led me to believe that you might have erred in equating
10000(1-.07*150/360) with 9300 when you might have instead posted

"To keep it simple, all I was trying to say is that these 2 loans are identical:
1: discount 10000 by 7% leaving 9300 loan proceeds, single payment 10000 in 1 year
2: borrow 9300, and agree to repayment being a single payment of 10000 in 1 year"