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A bank offers an interest of 5% per annum compounded annua

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adbos912
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Re: A bank offers an interest of 5% per annum compounded annua [#permalink] New post   04 Aug 2020, 12:53
dont think we even need the principal amount

Amount earned in 4th year --> p(21/20)^4
Amount earned in 5th year --> p(21/20)^5

Ratio --> 20/21 --> find the proportional ratio that is in the answers.

Option C: 100:105

This value will be the same for any principal amount
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Re: A bank offers an interest of 5% per annum compounded annua [#permalink] New post   30 Nov 2021, 05:44
Hello,

Can anyone please explain how to go from 2nd to 3 rd year interest in detail please?

What I am doing wrong when jumping from the 2nd to 3rd year?

1st year interest: 10,000*(5/100)=500
2nd year interest: 500 + 500*0.05= 500(1.05)
3rd year interest: 500 + ((500(1.05))*0.05= 500*(1+1.05*0.05)=500*(1.0525)

Thanks a lot :)

emmak wrote:
A bank offers an interest of 5% per annum compounded annually on all its deposits. If $10,000 is deposited, what will be the ratio of the interest earned in the 4th year to the interest earned in the 5th year?

A. 1:5
B. 625:3125
C. 100:105
D. 100^4:105^4
E. 725:3225
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Re: A bank offers an interest of 5% per annum compounded annua [#permalink] New post   30 Nov 2021, 06:01
Hello,

Can anyone please explain how to go from 2nd to 3 rd year interest in detail please?

What I am doing wrong when jumping from the 2nd to 3rd year?

1st year interest: 10,000*(5/100)=500
2nd year interest: 500 + 500*0.05= 500(1.05)
3rd year interest: 500 + ((500(1.05))*0.05= 500*(1+1.05*0.05)=500*(1.0525)

Thanks a lot :)


I got it my bad

I was not adding the interest on the interest first year interest:

1st year interest: 10,000*(5/100)=500
2nd year interest: 500 + 500*0.05= 500(1.05)
Therefore your total money now is: 500+500(1.05)
3rd year interest: 500+ (500+500*1.05)*0.05= 500*1.05^2


emmak wrote:
A bank offers an interest of 5% per annum compounded annually on all its deposits. If $10,000 is deposited, what will be the ratio of the interest earned in the 4th year to the interest earned in the 5th year?

A. 1:5
B. 625:3125
C. 100:105
D. 100^4:105^4
E. 725:3225
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Re: A bank offers an interest of 5% per annum compounded annua [#permalink] New post   01 Dec 2021, 01:31
Suppose if we want to calculate total interest earned in 4 years i.e interest of (1st year + 2nd year + 3rd year + 4th year)

we use : P*(1+R/100)^n - P

If we want to calculate only for the interest in 4th-year

P*(1+R/100)^4 - P - P*(1+R/100)^3 - P (Gives only the Interest)

For the problem given we have used a ratio of Principle + Interest ( common term = principle )

or we can use the (Principle*(1+Interest)^4) / (Principle +(1+Interest)^5) ;
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Re: A bank offers an interest of 5% per annum compounded annua [#permalink] New post   24 Feb 2024, 15:02
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Re: A bank offers an interest of 5% per annum compounded annua [#permalink]
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