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Lolaergasheva
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If $1 were invested at 8 percent interest compounded annually, the Updated on: 02 Dec 2022, 01:37
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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B
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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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B
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If $1 were invested at 8 percent interest compounded annually, the 17 May 2017, 06:04
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If 1$ 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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If $1 were invested at 8 percent interest compounded annually, the 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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If $1 were invested at 8 percent interest compounded annually, the 19 May 2017, 06:24
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Lolaergasheva
If 1$ 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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If $1 were invested at 8 percent interest compounded annually, the 12 Oct 2017, 15:55
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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:
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B

Cheers,
Brent
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If $1 were invested at 8 percent interest compounded annually, the 20 Oct 2020, 09:22
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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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If $1 were invested at 8 percent interest compounded annually, the 18 Oct 2022, 00:38
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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:
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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If $1 were invested at 8 percent interest compounded annually, the 18 Oct 2022, 07:43
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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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If $1 were invested at 8 percent interest compounded annually, the 18 Oct 2022, 13:39
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Brilliant thanks BrentBrentGMATPrepNow for the clarification. Great examples and make a lot of sense now.
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If $1 were invested at 8 percent interest compounded annually, the 02 Dec 2023, 06:23
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