If $1 were invested at 8 percent interest compounded annually, the

Question

If $1 were invested at 8 percent interest compounded annually, the total value of the investment, in dollars, at the end of 6 years would be

A.  (1.8)^6

B.  (1.08)^6

C.  6(1.08)

D.  1 + (0.08)^6

E.  1 + 6(0.08)

sashiim20 · Accepted Answer

If 1$ were invested at 8% interest compounded annually, the total value of the investment at the end of 6 years would be:

Amount = P $(1+\frac{r}{100})^n$

P = Principal, r = rate of interest, n = number of years.
P = $1, r = 8% , n = 6 years

Amount = 1$(1+\frac{8}{100})^6$ = 1$(\frac{108}{100})^6$ = 1$(1.08)^6$ = $(1.08)^6$
Answer B...

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fluke · Answer

Q: What is the future value of $1 after 6 years; if it incurs compound interest every year once.

Formula:
 FV = PV(1+\frac{r}{n})^{nt}

where,
 FV= Future Value 
 PV= Present Value = $1 
 r= interest rate = 8% = 0.08 
 n=frequency of interest application to the value per year = 1(if compunded annually); it means that 8% interest is applied only once a year. 
 t=time (in years)=6

FV = PV(1+\frac{r}{n})^{nt} 
 FV = 1(1+\frac{0.08}{1})^{1*6} 
 FV = 1(1+0.08)^6 
 FV = (1.08)^6

Ans: "B"

ScottTargetTestPrep · Answer

Using the compound interest formula, we have:

future value = present value(1 + rate/n)^nt

(in which n = number of compounding periods in a year and t = total number of years)

future value = 1(1 + 0.08/1)^(1)(6)

future value = (1.08)^6

Answer: B

BrentGMATPrepNow · Answer

You can use this formula to calculate compound interest:
  Final balance = P( 1 + r/c)^nc   where:
P = the principal (the initial investment)
r = the  annual  interest rate  expressed as a decimal 
c = the number of times the interest is compounded each year 
n = the number of years the investment collects interest

For this question, P = $1, r = 0.08, c = 1, n = 6
So, the FINAL BALANCE = 1( 1 + 0.08/1)^ 
= (1.08)^6
Answer:  B

Cheers,
Brent

Hovkial · Answer

OFFICIAL GMAT EXPLANATION

Since the 8 percent interest is compounded annually, each year 0.08 times the investment is added to the investment. This is the same as multiplying the investment by 1.08. Therefore, after six years the initial investment of $1 is (1)(1.08)^6 dollars. Thus, the best answer is B.

Kimberly77 · Answer

Hi  BrentGMATPrepNow , on a side note that 8 percent interest compounded annually = 8 percent simple annual interest rate here? So the end calculation is also same (1.08)^6 ?

BrentGMATPrepNow · Answer

If an N-dollar investment is  compounded  annually at 8%, then after 6 years, the value of the investment = (N)(1.08)^6 ≈  1.85N  dollars
If an N-dollar investment has a  simple annual interest rate  of 8%, then after 6 years, the value of the investment = 1.08N + 1.08N + 1.08N + 1.08N + 1.08N + 1.08N =  1.48N  dollars

Kimberly77 · Answer

Brilliant thanks Brent BrentGMATPrepNow  for the clarification. Great examples and make a lot of sense now.

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