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A sum of money was lent for two years at 20% compound interest

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A sum of money was lent for two years at 20% compound interest  [#permalink]

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New post 18 Feb 2018, 04:42
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A
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C
D
E

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A sum of money was lent for two years at 20% per annum compound interest. If the interest on the sum for the second year was $1440, find the sum.
A) $3000
B) $5000
C) $6000
D) $9000
E) $12000

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Re: A sum of money was lent for two years at 20% compound interest  [#permalink]

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New post 18 Feb 2018, 08:19
souvonik2k wrote:
A sum of money was lent for two years at 20% per annum compound interest. If the interest on the sum for the second year was $1440, find the sum.
A) $3000
B) $5000
C) $6000
D) $9000
E) $12000


If x is the amount that is lent, the interest compounded for the first year at 20% is \(0.2x\)
However, for the second year the interest is calculated on \(x + 0.2x = 1.2x\)
The interest calculated for the second year is \(0.2*1.2x = 0.24x\)

Now \(0.24x = 1440 -> x = \frac{1440}{0.24} = \frac{1440*100}{24} = $6000\)

Therefore, the sum of money that was lent is $6000(Option C)
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A sum of money was lent for two years at 20% compound interest  [#permalink]

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New post 19 Feb 2018, 20:32
souvonik2k wrote:
A sum of money was lent for two years at 20% per annum compound interest. If the interest on the sum for the second year was $1440, find the sum.
A) $3000
B) $5000
C) $6000
D) $9000
E) $12000

Answer choices

Start with Answer C to get a benchmark. (If C is too great, D and E are also too great. If C is too low, A and B are also too low.)

Answer C) $6,000

If amount lent was $6,000, at 20 percent compounding interest:

At the end of Year 1, the TOTAL AMOUNT (base PLUS interest) would be

($6,000)(1.2) = $7,200 OR
$6,000 + (.20)($6,000)=
$6,000 + $1,200 = $7,200

Interest payment for Year 2?

This time we care only about interest paid. (It is the only real amount we have.)

Base amount is now $7,200
Does interest paid for Year 2 = $1,440?

Base for Year 2: $7,200
Interest: 20 percent of $7,200 gets paid
Interest paid: $7,200 * (.20) = $1,440. Bingo

Answer C

Compound interest rate formula
Another approach is to work backwards from the amount at the end of two years, using compound interest formula.

Compound interest rate formula:
\(A = P(1 + \frac{r}{100})^{n*t}\)

End of Year 1?
\(A = P(1.2)^1\)
\(A = 1.2P\)


End of Year 2?
\(A = P(1.2)^2\)
\(A = 1.44P\)

\(1.44P - 1.2P = .24P\)
\(.24P = $1,440\)

\(P =
\frac{$1,440}{.24}=\frac{$144,000}{24}=$6,000\)


Answer C
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A sum of money was lent for two years at 20% compound interest   [#permalink] 19 Feb 2018, 20:32
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