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Nathan took out a student loan for 1200$ at 10 percent annual interest

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Ryerson (Ted Rogers) Thread Master
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Nathan took out a student loan for 1200$ at 10 percent annual interest [#permalink]

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New post 22 Dec 2015, 21:18
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Question Stats:

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Nathan took out a student loan for 1200$ at 10 percent annual interest, compounded annually. If he did not repay any of the loan or interest during the first 3 years, which of the following is the closest to the amount of interest he owed for the 3 years.

A. 360
B. 390
C. 400
D. 410
E. 420
[Reveal] Spoiler: OA

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Re: Nathan took out a student loan for 1200$ at 10 percent annual interest [#permalink]

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New post 22 Dec 2015, 21:27
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RSOHAL wrote:
Nathan took out a student loan for 1200$ at 10 percent annual interest, compounded annually. If he did not repay any of the loan or interest during the first 3 years, which of the following is the closest to the amount of interest he owed for the 3 years.

A. 360
B. 390
C. 400
D. 410
E. 420


a straight Qrequiring direct formulae..
when compounded annualy the final amount=P(1+ r/100)^n..
here P=1200, r=10 and n=3..
1200(1+ 10/100)^3..
1200*1.1^3=1597.2


interest =1597-1200=397, which is nearly 400 in the choices given
ansC
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Re: Nathan took out a student loan for 1200$ at 10 percent annual interest [#permalink]

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Re: Nathan took out a student loan for 1200$ at 10 percent annual interest [#permalink]

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New post 12 May 2017, 01:41
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CI = \(1200 * (1+\frac{10}{100})^3\)

= \(1200* (1.10)^3\)

= 1200 * 1.331

= 1597.2


Approx amount = 1597.2 - 1200 = 397.8 = 400 (approx)

Explanation


C.I = P * \((1+\frac{r}{100*n})^nt\)

where,
P = principal amount
r = rate of Interest
n= number of times interest compounded
t = time period.


So, we have

n = 1200
r = 10
n = 1 (compounded annually)
t = 3 years.

Substitute above values in CI formula.


Ans: Option C

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Re: Nathan took out a student loan for 1200$ at 10 percent annual interest [#permalink]

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New post 12 May 2017, 02:33
RSOHAL wrote:
Nathan took out a student loan for 1200$ at 10 percent annual interest, compounded annually. If he did not repay any of the loan or interest during the first 3 years, which of the following is the closest to the amount of interest he owed for the 3 years.

A. 360
B. 390
C. 400
D. 410
E. 420


Principal amount is : 1200
Total amount after
1st yr = 1200 x 1.1 = 1320
2nd yr = 1320 x 1,1 = 1452
3rd yr = 1452 x 1.1 = 1597.2

Amount of interest he owed after 3 years = 1597.2 - 1200 = 397.2 ....... The closest value is 400.

[Reveal] Spoiler:
Correct Answer C

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Re: Nathan took out a student loan for 1200$ at 10 percent annual interest [#permalink]

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New post 15 May 2017, 09:35
when compounded annualy the final amount=P(1+ r/100)^n..
here P=1200, r=10 and n=3..
1200(1+ 10/100)^3..
1200*1.1^3=1597.2


final amount - P = P(1+ r/100)^n - P = Compound Interest

1597.2-1200 = :) aprox (397)= :-D aprox (400)
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Re: Nathan took out a student loan for 1200$ at 10 percent annual interest [#permalink]

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New post 26 May 2017, 04:26
RSOHAL wrote:
Nathan took out a student loan for 1200$ at 10 percent annual interest, compounded annually. If he did not repay any of the loan or interest during the first 3 years, which of the following is the closest to the amount of interest he owed for the 3 years.

A. 360
B. 390
C. 400
D. 410
E. 420


I did it this way:
1st year's interest: 10% of 1200=120,
2nd year's interest: 10% of 1320=132, ( here, 1320= 1200 +120),
3rd year's interest: 10% of 1452= 145.2 ( 1452= 1320+132)
hence total interest= \(397.2\approx{400}\)

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Re: Nathan took out a student loan for 1200$ at 10 percent annual interest [#permalink]

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New post 22 Jul 2017, 06:54
Question asked approximation so it is easy
Initial amount 1200 mean at year 1 end==120$(interest)
Now amount 1320 mean at year 2 end==(120+132)
now amount 1452 mean at year 3 end==(120+132+145.2)
total=397.2 close to 400
Option C

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Re: Nathan took out a student loan for 1200$ at 10 percent annual interest [#permalink]

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New post 12 Aug 2017, 08:22
RSOHAL wrote:
Nathan took out a student loan for 1200$ at 10 percent annual interest, compounded annually. If he did not repay any of the loan or interest during the first 3 years, which of the following is the closest to the amount of interest he owed for the 3 years.

A. 360
B. 390
C. 400
D. 410
E. 420


Closer to 400 than 390.
I doubt whether these qstns do come in exam.
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Re: Nathan took out a student loan for 1200$ at 10 percent annual interest   [#permalink] 12 Aug 2017, 08:22
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