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If $10,000 is invested at 8 percent annual interest, compounded semiannually, what is the balance after 5 year, in terms of dollars? A. $$10,000(1+ \frac{0.08}{2})^{10}$$ B. $$10,000(1+0.08)^5$$ C. $$10,000(1+0.08)$$ D. $$10,000(1-0.08)^2$$ E. $$10,000*1.08$$ _________________ Math Expert V Joined: 02 Aug 2009 Posts: 7959 Re: If$10,000 is invested at 8 percent annual interest, compounded semian  [#permalink]

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MathRevolution wrote:
If $10,000 is invested at 8 percent annual interest, compounded semiannually, what is the balance after 5 year, in terms of dollars? A. $$10,000(1+ \frac{0.08}{2})^{10}$$ B. $$10,000(1+0.08)^5$$ C. $$10,000(1+0.08)$$ D. $$10,000(1-0.08)^2$$ E. $$10,000*1.08$$ Whenever an amount is compounded semi-annually, the interest rate becomes half and TIME becomes two times.. So 1) Rate becomes 0.08/2 2) Time becomes 5*2=10 A is correct _________________ Senior PS Moderator V Joined: 26 Feb 2016 Posts: 3341 Location: India GPA: 3.12 Re: If$10,000 is invested at 8 percent annual interest, compounded semian  [#permalink]

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Compound interest = $$Amount * (1 + \frac{ROI}{100})^n$$
where
ROI is the rate of interest
n is the amount of years the amount is invested

When an amount is invested and interest is calculated semi-annually,
the rate of interest is halved and the number of years doubles.

The formula for compound interest is :
Compound interest = $$Amount * (1 + \frac{ROI}{200})^{2n}$$

Coming to the problem in hand,
Amount : 10000$Interest(annual)-ROI : 8% = $$\frac{8}{100} = 0.08$$ Number of years-n : 5 Substituting these values, Interest = $$10,000(1+ \frac{0.08}{2})^{10}$$ (Option A) _________________ You've got what it takes, but it will take everything you've got Senior SC Moderator V Joined: 22 May 2016 Posts: 3544 If$10,000 is invested at 8 percent annual interest, compounded semian  [#permalink]

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MathRevolution wrote:
If $10,000 is invested at 8 percent annual interest, compounded semiannually, what is the balance after 5 year, in terms of dollars? A. $$10,000(1+ \frac{0.08}{2})^{10}$$ B. $$10,000(1+0.08)^5$$ C. $$10,000(1+0.08)$$ D. $$10,000(1-0.08)^2$$ E. $$10,000*1.08$$ The formula for compound interest can be written in a few ways. IMO, the version that matches the answer choices most closely is A = P $$(1+ \frac{r}{n})^{nt}$$ A= amount of money accumulated over t years, including interest (what the question asks for) P = initial amount invested r = annual rate of interest in decimal form n = the number of times the interest is compounded annually t = number of years the amount is deposited (or borrowed) for nt = # of times per year interest is compounded times # of years P =$10,000
r = .08
n = 2 (semi-annually = twice per year)
t = 5 (years)
$$\frac{r}{n}$$ = $$\frac{.08}{2}$$
nt = 2*5 = 10

Using figures above, the equation becomes
A = $$10,000(1+ \frac{0.08}{2})^{10}$$

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MathRevolution wrote:
==> if it is invested at 8 percent annual interest and is compounded semiannually, From
10,000(1+8%$$(\frac{1}{2}))^{2*5}= 10,000(1+)^{10}$$ the answer is A

MathRevolution, your final step is incomplete. Please correct the solution!
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GMAT 1: 620 Q46 V29 Re: If $10,000 is invested at 8 percent annual interest, compounded semian [#permalink] Show Tags 1 generis wrote: MathRevolution wrote: If$10,000 is invested at 8 percent annual interest, compounded semiannually, what is the balance after 5 year, in terms of dollars?

A. $$10,000(1+ \frac{0.08}{2})^{10}$$
B. $$10,000(1+0.08)^5$$
C. $$10,000(1+0.08)$$
D. $$10,000(1-0.08)^2$$
E. $$10,000*1.08$$

The formula for compound interest can be written in a few ways. IMO, the version that matches the answer choices most closely is

A = P $$(1+ \frac{r}{n})^{nt}$$

A= amount of money accumulated over t years, including interest (what the question asks for)
P = initial amount invested
r = annual rate of interest in decimal form
n = the number of times the interest is compounded annually
t = number of years the amount is deposited (or borrowed) for
nt = # of times per year interest is compounded times # of years

P = $10,000 r = .08 n = 2 (semi-annually = twice per year) t = 5 (years) $$\frac{r}{n}$$ = $$\frac{.08}{2}$$ nt = 2*5 = 10 Using figures above, the equation becomes A = $$10,000(1+ \frac{0.08}{2})^{10}$$ Answer A A slightly modified formula. Just for ease of use. A = P $$(1+ \frac{r}{100n})^{nt}$$ Re: If$10,000 is invested at 8 percent annual interest, compounded semian   [#permalink] 10 Sep 2018, 07:37
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