Got this wrong on an official practice test. Resolving here for retention:
Method 1 - Plug-in values for x (quickest method)
x= 20
Compounded
New balance after compounding is equal to 1000(1+20/200)^2
= 1000(11/10)^2
= 1000(121/100)
= 1210
Simple interest
New balance with interest 1000(1+20/100)^1
= 1000(6/5)
= 1200
'How much more interest' = 1210 - 1200 = 10 more
Plug-in 20 to each answer choice to get 10
A - 5(20) = 200 --> Wrong
B - 10(20) = 200 --> wrong
C - (20)^2/ 20 = 20 --> wrong
D - (20)^2/40 = 10 --> correct
E - (10(2) + (20)^2/40) = 30 --> wrong
Method 2 - Algebraic, but since we have variables, breakdown the compounding periods instead of calculating it all in one go)
Compounding:
1000(1+x/100/2)^1
= 1000 (1 + x/200)^1
= 1000 + 5x
New balance after first compounding period = 1000 + 5x
Second compounding period
Principle *(Interest rate/#compound periods + 1)^compounding period
(1000 + 5x)(1 + x/200)^1
= 1000 + 5x + 5x + (5x^2)/200
= 1000 + 10x + x^2/40
Now we need to eliminate the principle to get the interest portion
= 1000 + 10x + x^2/40 - 1000
= 10x + x^2/40
Simple interest amount
1000(1+ x/100)^1
= 1000 + 10x
Interest portion = 1000+10x - 1000
= 10x
How much more interest?
= 10x + x^2/40 - 10x
= x^2/40
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Goal: Q49, V41
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