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Lolaergasheva
If 1$ were invested at 8% interest compounded annually, the total value of the investment 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)

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
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Lolaergasheva
If $1 were invested at 8 percent interest compounded annually, the total value of 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. \(1 + 6(0.08)\)

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)^[(6)(1)]
= (1.08)^6
Answer:
Cheers,
Brent
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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.
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BrentGMATPrepNow
Lolaergasheva
If $1 were invested at 8 percent interest compounded annually, the total value of 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. \(1 + 6(0.08)\)

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)^[(6)(1)]
= (1.08)^6
Answer:
Cheers,
Brent


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 ?
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Kimberly77
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 ?

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