True Discount problem

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Chinn_asama: Senior | Next Rank: 100 Posts; Posts: 77; Joined: Sat Jun 02, 2012 7:14 pm; Thanked: 1 times

True Discount problem

by Chinn_asama » Tue Jun 26, 2012 5:10 am

Hi

Q. The true discount on a certain sum of money due 3 years hence is $ 200 and the simple interest on the same sum for the same time and at the same rate is $240. Find the sum and the rate per cent.

First of all, what is true discount? Could anyone explain?

Thanx.

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Source: Beat The GMAT — Quantitative Reasoning | Tue Jun 26, 2012 5:10 am

KapTeacherEli: GMAT Instructor; Posts: 578; Joined: Tue Aug 25, 2009 6:00 pm; Thanked: 136 times; Followed by:62 members

by KapTeacherEli » Tue Jun 26, 2012 8:23 am

Chinn_asama wrote:Hi

Q. The true discount on a certain sum of money due 3 years hence is $ 200 and the simple interest on the same sum for the same time and at the same rate is $240. Find the sum and the rate per cent.

First of all, what is true discount? Could anyone explain?

Thanx.

Hi Chinn,

The "True discount" is a term used when you are promised a given amount of money in the future. Since money collect interest, the actual value of that promise is less than the face value. So, if the interest rate were 10% and I promised you $110 next year, than that's worth $100 THIS year since it would collect one year's interest. The true discount is $10.

In this case, the note is worth some Face Value in three years at interest rate r, Face Value = (1 + r)^3*Principal, and Face Value - Principal = true discount = $200.

However, I've never seen the term "true discount" tested on the GMAT--and the definition of the term that I looked up came from a 1913 dictionary, so I'm not sure the term is even in use! Also, the "true discount" is generally calculated with compound interest, but the problem doesn't specify whether we are using compound or simple interest to find it. Is this question from an official source?

Eli Meyer
Kaplan GMAT Teacher
Cambridge, MA
www.kaptest.com/gmat