I am trying to understand the explanation for couple of questions in the "The official guide for GMAT review", 10thedition.
Question 125) If $1 were invested at 8% interest compounded annually, the total value of the investment, at the end of 6years would be?
The answer says (1)(1.08)power6 = 1.08 to the power 6
0.05*10 to the power m-k = 5*10 to the power -2 *10 to the power m-k
I thought this should be 5*10 to the power 2 *10 to the power m-k (and not -2)
Sorry if it is a no brainer!
Appreciate your response.
This is how compound interest works. Here is a general example. Let's say you start off with X dollar and the interest rate is i%. After the first year, your have (X)(1 + i) dollars right? At the end of the second year, you get somemore interest, but the interest is applied to the new dollar amount that you have. So now at the end of 2 years, you have ((X)(1 + i)) times (1 +i ) or (X)(1+i)^2. At the end of 3 years, you have ((X)(1 + i)^2 )(1 + i) or (X)(1+i)^3. So you see, if you start with X dollars and you get interest of i% compounded annually, you will have (X)(1 + i)^N dollars at the end of N years.
Former Senior Instructor, Manhattan GMAT and VeritasPrep
Vice President, Midtown NYC Investment Bank, Structured Finance IT
MFE, Haas School of Business, UC Berkeley, Class of 2005
MBA, Anderson School of Management, UCLA, Class of 1993