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Shawn invested one half of his savings in a bond that paid s [#permalink]
25 Oct 2006, 07:22

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Shawn invested one half of his savings in a bond that paid simple interest for 2 years and received $550 as interest. He invested the remaining in a bond that paid compound interest, interest being compounded annually, for the same 2 years at the same rate of interest and received $605 as interest. What was the value of his total savings before investing in these two bonds?

Re: Shawn invested one half of his savings in a bond that paid [#permalink]
09 Nov 2013, 12:23

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Re: Shawn invested one half of his savings in a bond that paid s [#permalink]
20 Nov 2013, 09:47

Expert's post

karlfurt wrote:

Shawn invested one half of his savings in a bond that paid simple interest for 2 years and received $550 as interest. He invested the remaining in a bond that paid compound interest, interest being compounded annually, for the same 2 years at the same rate of interest and received $605 as interest. What was the value of his total savings before investing in these two bonds?

Let the total amount invested be 2x. Now, we know that from half of it, he got 275$ per year for 2 years, and from the other half he got a total of 605$ over 2 years as Cumulative interest. Now, the amount of interest he got from the second year of cumulative interest : 605-275 = 330$

Thus, if the rate be r, then r*x*(1+r)=330.

Again, we know that2r*x = 550,

Thus,(1+r) = \frac{6}{5} \to r = \frac{1}{5}

Replacing this in the second equation, we get 2x = \frac{550}{r} = 550*5 = 2750

Re: Shawn invested one half of his savings in a bond that paid s [#permalink]
20 Nov 2013, 16:59

mau5 wrote:

karlfurt wrote:

Shawn invested one half of his savings in a bond that paid simple interest for 2 years and received $550 as interest. He invested the remaining in a bond that paid compound interest, interest being compounded annually, for the same 2 years at the same rate of interest and received $605 as interest. What was the value of his total savings before investing in these two bonds?

Let the total amount invested be 2x. Now, we know that from half of it, he got 275$ per year for 2 years, and from the other half he got a total of 605$ over 2 years as Cumulative interest. Now, the amount of interest he got from the second year of cumulative interest : 605-275 = 330$

Thus, if the rate be r, then r*x*(1+r)=330.

Again, we know that2r*x = 550,

Thus,(1+r) = \frac{6}{5} \to r = \frac{1}{5}

Replacing this in the second equation, we get 2x = \frac{550}{r} = 550*5 = 2750

A.

wait how did you know that (1+r) = \frac{6}{5}

also where do you get 2x = \frac{550}{r} = 550*5 = 2750 from? Is there a lot of work you did in your head?

Because if you sub in 1/5 for R, then you end up with 2x=550/(1/5) and then 2x=2750, and x=1375, not 2750...

Re: Shawn invested one half of his savings in a bond that paid s [#permalink]
20 Nov 2013, 22:57

Please explain: Let the total amount invested be 2x. Now, we know that from half of it, he got 275$ per year for 2 years, and from the other half he got a total of 605$ over 2 years as Cumulative interest. Now, the amount of interest he got from the second year of cumulative interest : 605-275 = 330$

I do not understand the the underlined statement; how to get it? please explain. Thanks. Simple interest formula: I = PRt 550 = PR2 550/2P = R

Compound interest formula: P + I = P(1+R)^t P + 605 = P(1+R)^2 P + 605 = P(1 + 2(550/2P) + (550/2P)^2) P + 605 = P + 550/2 + (550)^2/ 4P 55 = (550)^2/4P P = 2750

Re: Shawn invested one half of his savings in a bond that paid s [#permalink]
20 Nov 2013, 23:05

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This post received KUDOS

Expert's post

smartyman wrote:

Please explain: Let the total amount invested be 2x. Now, we know that from half of it, he got 275$ per year for 2 years, and from the other half he got a total of 605$ over 2 years as Cumulative interest. Now, the amount of interest he got from the second year of cumulative interest : 605-275 = 330$

I do not understand the the underlined statement; how to get it? please explain. Thanks.

Say you have 200 $. Half of it is getting you simple interest per year at 10% rate.Thus, the interest you earn for the first year : \frac{10}{100}*100 = 10 $

Now, the other half is getting you compound interest at 10%, where interest is again compounded annually.Thus, the interest from the first year : \frac{10}{100}*100 = 10 $

Now, suppose I told you that the total CI you got from the other half for 2 years was 40 $, then the interest you earned from the second year is nothing but : 40-10 = 30$

The same has been done above. Note that as the rate of interest and the time is the same for both CI and SI, the interest earned for the first year will be exactly same in either case.

Re: Shawn invested one half of his savings in a bond that paid s [#permalink]
09 Jan 2014, 05:30

1

This post was BOOKMARKED

karlfurt wrote:

Shawn invested one half of his savings in a bond that paid simple interest for 2 years and received $550 as interest. He invested the remaining in a bond that paid compound interest, interest being compounded annually, for the same 2 years at the same rate of interest and received $605 as interest. What was the value of his total savings before investing in these two bonds?

I understand that the interest paid per year from the simple interest was $275 (i.e. 550/2) and that the second years payment for the second year of the compound interest is $330 (i.e. 605 - 275) and thus the rate is 20% because (330/275=1.2)

Re: Shawn invested one half of his savings in a bond that paid s [#permalink]
09 Jan 2014, 06:19

Expert's post

TroyfontaineMacon wrote:

karlfurt wrote:

Shawn invested one half of his savings in a bond that paid simple interest for 2 years and received $550 as interest. He invested the remaining in a bond that paid compound interest, interest being compounded annually, for the same 2 years at the same rate of interest and received $605 as interest. What was the value of his total savings before investing in these two bonds?

I understand that the interest paid per year from the simple interest was $275 (i.e. 550/2) and that the second years payment for the second year of the compound interest is $330 (i.e. 605 - 275) and thus the rate is 20% because (330/275=1.2)

but

after that....I AM LOST!!!!

HELP HELP HELP

So, we know that Shawn received 20% of the amount he invested in a year. We also know that in one year Shawn received $275, thud 0.2x = $275 --> x = $1,375.

Since, he invested equal sums in his 2 bonds, then his total savings before investing was 2*$1,375 = $2,700.

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