|
|
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
17 Jun 2021, 02:30
Kudos
Bookmarks
A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
81% (01:34) correct
19%
(01:41)
wrong
based on 116
sessions
History
Date
Time
Result
Not Attempted Yet
At what interest rate per annum will a sum of money double itself in 8 years?
(A) 12 1/2%
(B) 13%
(C) 15%
(D) 17%
(E) 19%
(A) 12 1/2%
(B) 13%
(C) 15%
(D) 17%
(E) 19%
17 Jun 2021, 07:25
Kudos
Bookmarks
Bunuel
The question clearly needs to specify that it's talking purely about simple interest, since I think most people reading it would assume the interest compounds annually. If it doubles in 8 years, and we are adding the same amount every year (which is what happens with simple interest), then we need to add 1/8 of the investment each year, or 12.5%.
If the interest did compound annually, then it's impossible to answer precisely using GMAT methods. There is an estimate, used in financial math, called the "rule of 72" that says it should take 72/x years for money to double, where x is the percent interest rate, so, since 72/9 = 8, the answer in that situation would be *approximately* 9%, but that's not an exact value (the exact answer is very close to 9.05%). But the GMAT would never test the 'rule of 72' because it's not going to be familiar to all test takers.
17 Jun 2021, 07:42
Kudos
Bookmarks
Bunuel
Solution :
We are given,
- • The sum of money is doubled and,
• The time taken = 8 years
Let the sum of money(P) be x.
Then, the amount (A) = 2x (since the principal gets doubled)
Therefore, SI = A - P
- = 2x - x
= x
Now, SI =\(\frac{P * R * T}{100}\)
- ⟹ x =\(\frac{ x * R * 8}{100}\)
⟹ \(\frac{x * 100}{x * 8}\) = R
- ⟹ \(\frac{100}{8}\) = R
⟹ \(\frac{25}{2}\) = R
⟹ 12\(\frac{1}{2}\) = R
- ⟹ R = 12\(\frac{1}{2}\)%
Hence, the correct answer is Option A.
