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# Another annuity related question

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Manager
Joined: 19 Aug 2009
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26 Aug 2009, 04:16
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Pls explain
Q.
Inorder to buy a car, a man borrowed $180,000 on the condition that he had to pay 7.5% interest every year.He also agreed to repay the principal in equal annual instalments over 21 yrs. After a certain number of years, however , the rate of interest has been reduced to 7%. It is also known that at the end of the agreed period, he will have paid in all$ 270900 in interest.
For how many yrs does he pay at the reduced interest rate?

1. 7 yrs
2. 12 yrs
3. 14 yrs
4. 16 yrs
5. 15 yrs
Intern
Joined: 30 Jun 2009
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Re: Another annuity related question [#permalink]

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26 Aug 2009, 04:51
defoue wrote:
I would go for A.

My method :
270900 = 180000x0,07m + 180000x0,075n
270900 = 180000x0,07m+n + 180000x0,005n
270900 = 264600 + 180000x0,005n
6300 = 900n
n=7

Does it sound logical??? or am I totally wrong???
Manager
Joined: 19 Aug 2009
Posts: 79
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Kudos [?]: 223 [0], given: 46

Re: Another annuity related question [#permalink]

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26 Aug 2009, 05:01
defoue wrote:
defoue wrote:
I would go for A.

My method :
270900 = 180000x0,07m + 180000x0,075n
270900 = 180000x0,07m+n + 180000x0,005n
270900 = 264600 + 180000x0,005n
6300 = 900n
n=7

Does it sound logical??? or am I totally wrong???

Answer as per book- is option 3

The issue with this type of problems are as u pay ur 1st instalment, principal sum should reduce while calculating 2nd instalment...we will have to take that into consideration

Try solving the problem i had posted under 'interests and instalments'...it also follows similar logic

If somebody can pls solve and explain??
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Re: Another annuity related question [#permalink]

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26 Aug 2009, 09:41
Every one solved correctly for n= 7

But you need to look at what is being asked, how may years did he pay at a reduced rate or at 7%

21-7 = 14 Years, Answer is 3
Intern
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Re: Another annuity related question [#permalink]

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27 Aug 2009, 03:37
deepak115 wrote:
Every one solved correctly for n= 7

But you need to look at what is being asked, how may years did he pay at a reduced rate or at 7%

21-7 = 14 Years, Answer is 3

Thx Deepak,
I hate doing those errors....
Manager
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Re: Another annuity related question [#permalink]

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20 Sep 2009, 04:37
1
KUDOS
nice Q. C it is.

13500x+12600y=270900
x+y=21
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Re: Another annuity related question   [#permalink] 20 Sep 2009, 04:37
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