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Schools: Warrington (S)
Posts: 226
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Difficulty:
55%
(hard)
Question Stats:
64% (02:10) correct
36%
(02:10)
wrong
based on 179
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An investment of \(P\) dollars earns a simple annual interest rate of R percent over a time period of \(T\) years. If the annual interest rate is increased by 60 percent, then the time required to earn the same amount of interest would be reduced by what percent?
(A) 62.5%
(B) 60%
(C) 40%
(D) 37.5%
(E) 30%
(A) 62.5%
(B) 60%
(C) 40%
(D) 37.5%
(E) 30%
Posts: 12
Ans (A) is the trap
SI = P*R*T1/100 (old rate) -----(1)
SI = P*1.6R*T2/100 (new rate) -----(2)
where T1 and T2 are the respective times
Equate (1) and (2) since SI is equal
After equating both sets of equations :
T(new) = 10/16 T(old) ~~ 5/8 = 0.625
To calculate the % decrease:
1-0.625/1 * 100 = 37.5 %. Ans (D)
SI = P*R*T1/100 (old rate) -----(1)
SI = P*1.6R*T2/100 (new rate) -----(2)
where T1 and T2 are the respective times
Equate (1) and (2) since SI is equal
After equating both sets of equations :
T(new) = 10/16 T(old) ~~ 5/8 = 0.625
To calculate the % decrease:
1-0.625/1 * 100 = 37.5 %. Ans (D)
HoudaSR
Joined: 08 Aug 2022
Last visit: 24 Nov 2023
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Location: Morocco
Schools: HBS '26 Oxford Said'25 Judge '25 Rotterdam'25 Yale '24
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Schools: HBS '26 Oxford Said'25 Judge '25 Rotterdam'25 Yale '24
Posts: 71
Simple interest= Principle (P) x Interest rate (R) x time (T). If R is to be increased by 60 that means we will have to multiply it by 160%, and in order to maintain the same amount of interest, we will need to divide also by 160%.
Hence, SI=P x R x 160% x T/160%.
and 160%= 160/100= 16/10= 8/5.
Which means that we will have to multiply T by the reciprocal of 8/5.
Thus, SI= P x R x 8/5 x (T x 5/8).
If T is multiplied by 5/8, that means that T is reduced by (1-(5/8)= 3/8).
3/8= 0,375= 37,5%
The correct answer is D.
Hence, SI=P x R x 160% x T/160%.
and 160%= 160/100= 16/10= 8/5.
Which means that we will have to multiply T by the reciprocal of 8/5.
Thus, SI= P x R x 8/5 x (T x 5/8).
If T is multiplied by 5/8, that means that T is reduced by (1-(5/8)= 3/8).
3/8= 0,375= 37,5%
The correct answer is D.
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