Latest GRE Aptitude Question SOLUTION: A college student expects to earn at least $1,000 in interest on an initial investment of $20,000. If the money is invested for one year at interest compounded quarterly, what is t

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(#M40105907) GRE Numerical Ability question Keep an EYE

A college student expects to earn at least $1,000 in interest on an initial investment of $20,000. If the money is invested for one year at interest compounded quarterly, what is the least annual interest rate that would achieve the goal?

Asked In GRE Jaspalsingh Parmar (9 years ago)

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Flambo  (9 years ago)

Basically we are asked to find the minimum rate of interest for $20,000 under compound interest compounding quarterly such that the student can earn at least $1000. So, the student is expected to have at least $21,000 (Initial amount + Interest) after one full year.

By compound interest formula,

C.I = A * [1+(Rate in decimal/ # (Number) of Compounding)]^(# of Years * # of Compounding)
21000 = 20000 * [1 + (R/400)]^4 ........# of compounding is 4 and rate in decimal, so R/400
1.05 = [1 + (R/400)]^4
Raising to power 1/4 on both sides of the above equation,
(1.05)^(1/4) = [1 + (R/400)] ......4 * (1/4) = 1 on right side
1.0123 ≃ 1+ (R/400) ......While using GRE calculator take square root of 1.05 twice
0.0123 ≃ R/400
R ≃ 4.92

To earn a interest of $1000, the rate of interest should be 4.92% approx but the problem says "atleast" $1000.
So, the rate of interest should be greater than $1000 to meet the students expectation.

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Flambo  (9 years ago)

Edit: So, the rate of interest should be greater than 4.92% to meet the students expectation.

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