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

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If $1 were invested at 8 percent interest compounded annually, the  [#permalink]

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New post Updated on: 25 May 2017, 13:28
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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. \(1 + 6(0.08)\)
Spoiler: OA

Originally posted by Lolaergasheva on 08 Feb 2011, 04:48.
Last edited by Bunuel on 25 May 2017, 13:28, edited 1 time in total.
Renamed the topic and edited the question.
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Re: If $1 were invested at 8 percent interest compounded annually, the  [#permalink]

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New post 08 Feb 2011, 05:18
1
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]

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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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Re: If $1 were invested at 8 percent interest compounded annually, the  [#permalink]

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New post 19 May 2017, 06:24
1
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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If $1 were invested at 8 percent interest compounded annually, the  [#permalink]

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New post 12 Oct 2017, 15:55
Top Contributor
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:
Spoiler: ::
B


Cheers,
Brent
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