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If a sum of money invested at compound interest amounts to $800 in 3

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Bunuel
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If a sum of money invested at compound interest amounts to $800 in 3 [#permalink] New post   22 Oct 2020, 12:39
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If a sum of money invested at compound interest amounts to $800 in 3 years and to $840 in 4 years, what is the rate of interest per annum?

A. 2%
B. 4%
C. 5%
D. 8%
E. 10%
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C
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Re: If a sum of money invested at compound interest amounts to $800 in 3 [#permalink] New post   22 Oct 2020, 15:30
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Bunuel wrote:
If a sum of money invested at compound interest amounts to $800 in 3 years and to $840 in 4 years, what is the rate of interest per annum?

A. 2%
B. 4%
C. 5%
D. 8%
E. 10%


Between the timeline of t = 3 and t = 4 is only 1 year, and with that 1 year we have a principle of $800 accumulating to $840. Therefore in that one year, 40 was earned as interest with a principle of 800. Then the annual interest rate would be 40/800 = 5%. (If it was two years we would square root 840/800 then subtract 1).

Ans: C
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Re: If a sum of money invested at compound interest amounts to $800 in 3 [#permalink] New post   27 Oct 2020, 11:12
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Bunuel wrote:
If a sum of money invested at compound interest amounts to $800 in 3 years and to $840 in 4 years, what is the rate of interest per annum?

A. 2%
B. 4%
C. 5%
D. 8%
E. 10%

Solution:

We see that the amount of interest for the 4th year is 840 - 800 = $40. So the annual interest rate (assume the interest is compounded annually) is 40/800 = 5/100 = 5%.

Answer: C
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Re: If a sum of money invested at compound interest amounts to $800 in 3 [#permalink] New post   30 Oct 2020, 13:45
840/x^4 = 800/x^3

x^3 * 840 = 800 * x^4

840 = 800 * x

x = 21/20

x = 1.05

=>

5%
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Re: If a sum of money invested at compound interest amounts to $800 in 3 [#permalink]
30 Oct 2020, 13:45
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