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

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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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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

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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
2
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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New post 12 May 2017, 01:41
1
1
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
1
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.

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.
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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 08 Aug 2018, 22:21
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


Please find the short calculation

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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 Feb 2019, 12:36
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


Since the 10% rate is compounded annually, the amount of interest increases by 10% each year:
First-year interest = 10% of 1200 = 120.
Second-year interest = (first-year interest) + 10% = 120 + 12 = 132.
Third-year interest = (second-year interest) + 10% = 132 + 13.2 = 145.2.
Total interest = 120 + 132 + 145.2 = 397.2.


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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 24 Feb 2019, 06:53
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


We can use the annual compound interest formula: A = P(1 + r)^t. So we have:

A = 1200(1 + 0.1)^3

A = 1200(1.1)^3

A = 1597.2

The amount of $1597.20 is the total amount (principal plus interest) he owes, so the amount of interest he owes is 1597.2 - 1200 = $397.2, or approximately $400.

Answer: C
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Re: Nathan took out a student loan for 1200$ at 10 percent annual interest   [#permalink] 24 Feb 2019, 06:53
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