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

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adbos912

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04 Aug 2020, 12:53

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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

Naptiste

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30 Nov 2021, 05:44

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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

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

Naptiste

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30 Nov 2021, 06:01

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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

[/quote]

Jatro

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01 Dec 2021, 01:31

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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) ;

SKaur3

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27 Nov 2024, 09:55

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I think this is the underlying concept used by Bunuel Solution.
Interest for n-th year:
Interest = An - An-1

After n years Interest for the nth year will be = P(1+r)^n
After n-1 years = P(1+r)^(n-1)

Interest for nth year = $P(1+r)^n - P(1+r)^{n-1} = P(1+r)^{n-1}[ 1+r -1] = P*r* (1+r)^{n-1}$

Ratio= $\frac{I_4 }{ I_5}$
Ratio= $\frac{P*r*(1+r)^3 }{ P*r*(1+r)^4 }$

r = 0.05
Ratio = $\frac{1}{1.05} = \frac{100}{105} $

Adarsh_24

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28 Dec 2024, 22:56

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Bunuel

emmak

The interest earned in the 1st year = $500
The interest earned in the 2nd year = $500*1.05
The interest earned in the 3rd year = $500*1.05^2
The interest earned in the 4th year = $500*1.05^3
The interest earned in the 5th year = $500*1.05^4

(500*1.05^3)/(500*1.05^4) = 1/1.05=100/105.

Answer: C.

I think I'm missing something
1st year: 500
2nd year: 500(from initial investment) + 500*5/100 (interest on previous year's interest) = 500 + 500* 5/100 = 500*1.05
3rd year: 500(from initial investment) + ( 500 + 500 * 5/100 ) 5/100 (intereset on previous year interest)
= 500 + 500 * 5/100 + 500 * (5/100)^2
= 500 ( 1 + 5/100 + (5/100)^2 )
The bracket is not quite 1.05^2.

What am I missing?

ok i get it now.
3rd year start should have interest up on interest for 1st and 2nd year.
500(from initial investment) + 500 * 5/100 (interest on first year interest) + ( 500 + 500 * 5/100 ) 5/100 (interest on 2nd year interest)
500 ( 1 + 5/100 + 5/100 + (5/100)^2)
500 (1+.05)^2

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