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

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Lolaergasheva
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If $1 were invested at 8 percent interest compounded annually, the [#permalink] New post  Updated on: 02 Dec 2022, 01:37
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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. \(1 + 6(0.08)\)
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Originally posted by Lolaergasheva on 08 Feb 2011, 04:48.
Last edited by Bunuel on 02 Dec 2022, 01:37, edited 2 times in total.
Renamed the topic and edited the question.
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sashiim20
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Re: If $1 were invested at 8 percent interest compounded annually, the [#permalink] New post  17 May 2017, 06:04
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If 1$ 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
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Re: If $1 were invested at 8 percent interest compounded annually, the [#permalink] New post  08 Feb 2011, 05:18
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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"
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Re: If $1 were invested at 8 percent interest compounded annually, the [#permalink] New post  19 May 2017, 06:24
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Lolaergasheva wrote:
If 1$ 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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BrentGMATPrepNow
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Re: If $1 were invested at 8 percent interest compounded annually, the [#permalink] New post  12 Oct 2017, 15:55
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Lolaergasheva wrote:
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:
Show Spoiler
B


Cheers,
Brent
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Re: If $1 were invested at 8 percent interest compounded annually, the [#permalink] New post  20 Oct 2020, 09:22
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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Kimberly77
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Re: If $1 were invested at 8 percent interest compounded annually, the [#permalink] New post  18 Oct 2022, 00:38
BrentGMATPrepNow wrote:
Lolaergasheva wrote:
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:
Show Spoiler
B


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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Re: If $1 were invested at 8 percent interest compounded annually, the [#permalink] New post  18 Oct 2022, 07:43
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Kimberly77 wrote:
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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I’ve spent the last 20 years helping students overcome their difficulties with GMAT math, and the biggest thing I’ve learned is…
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Kimberly77
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Re: If $1 were invested at 8 percent interest compounded annually, the [#permalink] New post  18 Oct 2022, 13:39
Brilliant thanks BrentBrentGMATPrepNow for the clarification. Great examples and make a lot of sense now.
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Re: If $1 were invested at 8 percent interest compounded annually, the [#permalink]
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