What amount, in dollars, invested for one year at an interest rate of

Question

What amount, in dollars, invested for one year at an interest rate of 2 percent compounded semiannually would produce the same final balance at the end of the year as $10,000 invested for one year at an interest rate of 4 percent compounded quarterly?

A. $10,000
B. $10,201
C. $10,500
D. $10,801
E. $20,000

Bunuel · Accepted Answer

First, we'll calculate the final balance of $10,000 invested at a 4 percent interest rate compounded quarterly. An annual rate of 4 percent compounded quarterly equates to 1 percent per quarter, applied 4 times a year (at the end of the 3rd, 6th, 9th, and 12th months). Therefore, the final balance after one year will be:

$10,000*(1+\frac{0.04}{4})^{1*4}=$10,000*(1.01)^{4}

For 2 percent compounded semiannually, which means 1 percent twice a year, the final balance at the year's end is:

$x*1.01^2

These two final balances need to be equal:

$x*1.01^2 = $10,000*1.01^{4} ;

$x = $10,000*1.01^2 ;

$x = $10,000*\frac{101^2}{100^2} ;

$x = 101^2 ;

$x = (100+1)^2 ;

$x = 100^2+2*100+1 ;

$x= 10,201 .

Answer: B.

Fish181 · Answer

Here's a handwritten explanation. You will have to know how to multiply and divide decimals on the exam (so I've been told). So important to learn this if you don't already know how.

Kinshook · Answer

Asked: What amount, in dollars, invested for one year at an interest rate of 2 percent compounded semiannually would produce the same final balance at the end of the year as $10,000 invested for one year at an interest rate of 4 percent compounded quarterly?

Let the amount be x dollars

x (1 + 2%/2)ˆ2 = 10000 (1 + 4%/4)ˆ4
x (1.01)ˆ2 = 10000 (1.01)ˆ4
x = 10000(1.01)ˆ2 = $10,201

IMO B

Let the amount be x dollars

x (1 + 2%/2)ˆ2 = 10000 (1 + 4%/4)ˆ4
x (1.01)ˆ2 = 10000 (1.01)ˆ4
x = 10000(1.01)ˆ2 = $10,201

IMO B

Bunuel · Answer

Similar questions also from GMAT Prep Focus: https://gmatclub.com/forum/what-amount- ... 23183.html https://gmatclub.com/forum/julio-deposi ... 25028.html

anjalic2503 · Answer

Bunuel  @
 KarishmaB 
when it says 'interest rate of 2 percent compounded semiannually' do we assume it is always annual interest rate? I thought is is compounded semiannually at 2 percent rate so P(1+2/100)^2

Bunuel · Answer

The question says: What amount, in dollars, invested for one year at an interest rate of 2 percent compounded semiannually ... So, we are directly told that 2 percent is per year rate. Here are two other questions fromGMAT Prep: 1. What amount, in dollars, invested for one year at a simple annual interest of 2 percent would earn the same amount of interest as $10,000 invested for one year at an annual interest rate of 4 percent compounded semiannually ? 2. Julio deposited $1,000 at an annual interest rate of 8 percent compounded semiannually , and Elena deposited $1,000 at a simple annual interest rate of x percent ... Here are these questions: https://gmatclub.com/forum/what-amount- ... 23183.html https://gmatclub.com/forum/julio-deposi ... 25028.html

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What amount, in dollars, invested for one year at an interest rate of

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