G.C.S..E Maths Question??

How do you work out this question?


"A woman invests £3000 over four years at 5% compound interest


Giving your answer to the nearest penny, work out the interest gained. "

G.C.S..E Maths Question??
This may help:-)
Reply:I think you need to work out 5% of £3000


Then work out 5% of that


then 5% of that and then 5% of that.





You then add together all the 5%'s





i think...





1.) 5% of 3000=150


3000+150=3150





2.) 5% of 3150=157.5


3150+157.5= 3307.5





3.) 5% of 3307.5=165.375


3307.5+165.375=3472.875





4.)5% of 3472.875=173.64375


3472.875+173.64375=3646.51875


______


5.) 3646.51875-3000 = 646.51875





=£646.52





Hope this is right, also help it makes sense and helps! :)








Other people seem to have a fancy formula - I just used simple maths haha. Oh well, we all appear to have similar answers!
Reply:after one year: 3000*.04 = 120


end of 2 years: 3120 *.04 = 124.80


end of 3 years: 3243.8*.04 = 129.75


end of 4 years: 3373.55*.04 = 134.94





total after 4 years is 3508.49





therefore total interest gained is 3508.49 - 3000 = 508.49





alternatively use a(1+r) to the par of n, all divided by n





where a = initial capital (3000O


r = rate of interest (4%)


n = no of years (4)




















sorry i did this at 4% by accident, but should be 5%... but u get my drift......
Reply:Year 1 £3000 + £150 interest (5%)


Year 2 £3150 + £157.50


Year 3 £3307.50 + £165.37


= £3472.87


Year 4 £3472.87 + £173.64 =£3646.51
Reply:1st year = £3000*5%=£150 so its £3150 for 1st year


2nd year = £3150*5%=£157.5 so its £3307.5 for the second year


3rd year = £3307.5*5%=£165.375 so its £3472.875 for the 3rd year


4th year = £3472.875*5%=£173.64375 so its 3646.51875 over the four years





so her intrest ganied would be £646.5 (3646.51875 - 3000 - rounded to 1 d.p. aka 1 penny)
Reply:Not too hard this really. Start from first principles.


let the initial amount £3000 be "A"


Interest rate 5% (but the MULTIPLIER would be 1.05) be "R"


let the no. or years (or term) be "N"





after yr 1 (N=1)total will be A x R





after yr 2 (N=2)total will be


(A x R) x R = AR^2 (that is R raised to the power of 2 (which is N the term no.)





after yr 3 (N=3) total will be the total after yr 2 MULTIPLYED by our R again ie:-


(AR^2) x R = AR^3 (this 3 is N, the term no. or no. of years.)





after yr 4 (N=4) total will be the total after yr3 MULTIPLYED by our R again ie:-


(AR^3) x R = AR^4 (this 4 is N, the term no. )





So, AR^N gives us the TOTAL figure.





Putting our figures in gives us the TOTAL:-





3000 x (1.05)^4 = 3646.51875 (£3646.52 for cash!)





The question asks for the INTEREST which is obviously this TOTAL minus the initial term £3000.





So the final answer is £646.52





Sum to N terms of a geometric progretion is ar^n (a is first term, r the rate or multiplyer, n the number of terms)
Reply:Value year n+1 = Value year n * (1 + interest).


Value year 5 = Value year 0 * (1 + interest) ^ 5 = 3000* (1.05 ^ 5) = 3000 * 1.276281562 = 3828.84 = more than i have.:)
Reply:£646.52
Reply:3000*(1.05^4)=£3646.52


3000 is the starting money, 1.05 is the interest (1*3000 + 5% of 3000) and 4 is the amount of years.
Reply:i am not sure if this is the correct method becasue i can't wuie remember but i think it might be...


3,000 x 0.05^4


then add this to 3,0000 to work out the overall value as this is just the interest