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# Sam invests a principal of $10,000, which earns interest ove  Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: GMAT Club Legend Joined: 07 Jun 2014 Posts: 4750 GRE 1: Q167 V156 WE: Business Development (Energy and Utilities) Followers: 93 Kudos [?]: 1665 [0], given: 396 Sam invests a principal of$10,000, which earns interest ove [#permalink]  30 Jul 2018, 10:34
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Question Stats:

68% (01:52) correct 31% (01:01) wrong based on 16 sessions
Sam invests a principal of $10,000, which earns interest over a period of years.  Quantity A Quantity B The final value of the investment after 2 years at 8% interest, compounded annually The final value of the investment after 4 years at 4% interest, compounded annually A) Quantity A is greater. B) Quantity B is greater. C) The two quantities are equal. D) The relationship cannot be determined from the information given. [Reveal] Spoiler: OA _________________ Sandy If you found this post useful, please let me know by pressing the Kudos Button Try our free Online GRE Test GMAT Club Legend Joined: 07 Jun 2014 Posts: 4750 GRE 1: Q167 V156 WE: Business Development (Energy and Utilities) Followers: 93 Kudos [?]: 1665 [0], given: 396 Re: Sam invests a principal of$10,000, which earns interest ove [#permalink]  12 Aug 2018, 07:10
Expert's post
Explanation

Solve this problem by applying the compound interest formula:
$$V=P(1+\frac{r}{100})^t$$

Since the principal P is the same in both cases, leave it out and just compare the rest:

Quantity A: $$(1+\frac{r}{100})^t=(1+\frac{8}{100})^2= (1.08)^2 = 1.08 × 1.08 = 1.1664$$

Quantity B: $$(1+\frac{r}{100})^t=(1+\frac{4}{100})^4= (1.04)^4 = 1.04×1.04×1.04×1.04 ≈ 1.1699$$

Quantity B is greater.
_________________

Sandy
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