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

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Status: Preparing for GMAT
Joined: 25 Nov 2015
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A sum of money was lent for two years at 20% compound interest  [#permalink]

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18 Feb 2018, 04:42
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55% (01:44) correct 45% (02:25) wrong based on 35 sessions

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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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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) _________________ You've got what it takes, but it will take everything you've got Senior SC Moderator Joined: 22 May 2016 Posts: 3077 A sum of money was lent for two years at 20% compound interest [#permalink] ### Show Tags 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

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?
$$A = P(1.2)^2$$
$$A = 1.44P$$

$$1.44P - 1.2P = .24P$$
$$.24P = 1,440$$

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

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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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