Simple & Compound Interest

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francoisph: Master | Next Rank: 500 Posts; Posts: 124; Joined: Sun Mar 07, 2010 3:15 pm; Thanked: 1 times

Simple & Compound Interest

by francoisph » Mon Jun 21, 2010 6:49 am

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?

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Source: Beat The GMAT — Problem Solving | Mon Jun 21, 2010 6:49 am

amising6: Master | Next Rank: 500 Posts; Posts: 294; Joined: Wed May 05, 2010 4:01 am; Location: india; Thanked: 57 times

by amising6 » Mon Jun 21, 2010 7:05 am

francoisph 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?

now another simple formula
diffrence between s.i and compound interest for 2 year=pr^2/100(only for 2 yaer)
c.i -s.i=pr^2/100
605-550=pr^2/100
need r to find the answer

need to check this formula

Last edited by amising6 on Mon Jun 21, 2010 7:14 am, edited 1 time in total.

Ideation without execution is delusion

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amising6: Master | Next Rank: 500 Posts; Posts: 294; Joined: Wed May 05, 2010 4:01 am; Location: india; Thanked: 57 times

by amising6 » Mon Jun 21, 2010 7:13 am

compound interest remain same as simple interest for first year
in second year compound interset=s.i+interest earned on S.i
605=550+((r/100)*550)
(55*100)/550=r
10=r

s.i=prt/100
550=(p*10*2)/100
550*5=p
principle=2750
answer

Ideation without execution is delusion

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tingle15: Newbie | Next Rank: 10 Posts; Posts: 3; Joined: Tue Jun 01, 2010 10:58 pm

by tingle15 » Mon Jun 21, 2010 11:28 am

@amising6: Please tell me if I derived the formula given by you correctly...

A = P[1+(R/100)]^2
A = P[1+(R/100)^2+(2R/100)]
A - P = P(R/100)^2 + (2PR/100)
A - P = (2PR/100) + [(2PR/100)(R)]/2*100
CI = SI + (1/2)*Interest on SI

605 = 550+(1/2)(550*R)/100

Hence R = 20%