Compound Interest

[Akansha]

Jim invested $1000 @ 10% compounded annually. Laura invested $2000
@ 5% compounded annually. Total interest of Jim is how much more than total
interest of Laura after 2 years?
a. 5
b. 15
c. 50
d. 100

OA is A

[pemdas]

compounded interest means interest also earns interest, so added to the base amount every time
interest in 1st year: Jim 1000*0.1=100; Laura 2000*0.05=100
interest 2nd year: 1100*0.1=110; Laura 2100*0.05=105
total Jim=100+110=210
total Laura=100+105=205
difference Jim-Laura=210-205=5, a)

Jim invested $1000 @ 10% compounded annually. Laura invested $2000
@ 5% compounded annually. Total interest of Jim is how much more than total
interest of Laura after 2 years?
a. 5
b. 15
c. 50
d. 100

OA is A

[Frankenstein]

Hi,
Jim's investment value at the end of 2 years = 1000.(1+0.1)^2 = 1210.
So, interest is 1210-1000 =210
Laura's investment value at the end of 2 years = 2000.(1+0.05)^2 = 2205.
So, interest is 2205-2000 =205
difference is 210-205=5

Hence, answer A

Cheers!

[cans]

Jim - 1000*(1.1)^2 - 1000 = 210
Laura - 2000*(1.05)^2 - 2000 = 205
hence difference in interest = 5
IMO A

[smackmartine]

IMO A

A would say this question is simply a test of how quickly you can do the % of amounts given.

Jim's interest:
10% of 1000 ---> 100 (1st Year)
10% of 1100 ---->110 (2nd Year)

Laura's interest:
5% of 2000 ---> (10% of 2000 )/2 --> 200/2 -->100 (1st Year)
5% of 2100 ---->(10% of 2100)/2 --> 210/2 --->105 (2nd Year)

Difference =(210 - 205)= 5

Its almost always very helpful and quick to get 10% or 1% of any # in order to calculate some % of bigger #.

For example 52% of 1500 can be calculated as (10% of 1500)*5 + (1% of 1500)*2 = (150*5+ 15*2)=750+30=780

[irock]

Total interest of Jim after 2 years = $(1000*1.1*1.1)-1000=$210

Total interest of Laura after 2 years = $(2000*1.05*1.05)-2000=$205

Hence, Total interest of Jim is more than total interest of Laura after 2 years by = $210 - $205 = $5

Answer is A.