Simple & Compound Interest

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

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

@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%

if r = 20% then:
20%/100% = $550/x, x = $2,750. Since this is half of his savings, then total savings = $2,750*2=$5,500

What is the OA?

principle=2750
answer

550 = P(20)(2)/100

P = 1375

The total savings would be 2*1375 = 2750