Question

question 1-8
how much more will account x be worth than account y after 20 years?

account x	account y

account x will be worth $\underline{\quad\quad\quad\quad\quad} more than account y after 20 years.

Explanation:

Step1: Calculate Account X value

Simple interest formula: $A = P(1 + rt)$.
$A_X = 8000(1 + 0.018×20) = 8000×1.36 = 10880$

Step2: Calculate Account Y value

$A_Y = 10000(1 + 0.02×20) = 10000×1.4 = 14000$

Step3: Find the difference

$A_Y - A_X = 14000 - 10880 = 3120$? Wait, no—wait, wait, reverse: the question says how much more X is than Y? Wait no, wait calculation again: 0.018×20=0.36, 8000×0.36=2880, so X total is 8000+2880=10880. Y: 0.02×20=0.4, 10000×0.4=4000, Y total=10000+4000=14000. So Y is more than X. Wait, maybe I misread the interest rates? Wait the problem says "how much more will account X be worth than account Y"—but according to calculation, Y is more. Wait no, maybe the interest rates are 18% and 2%? Oh! Oh, 1.8% vs 0.2%? Wait no, the user wrote 1.8% annual simple interest for X, 0.2% for Y? Wait let's check again: 1.8% is 0.018, 0.2% is 0.002. Oh! I made a mistake earlier—Y's rate is 0.2% not 2%.

Correct Step1: Recalculate Account X

$A_X = 8000(1 + 0.018×20) = 8000×1.36 = 10880$

Correct Step2: Recalculate Account Y

$A_Y = 10000(1 + 0.002×20) = 10000×1.04 = 10400$

Correct Step3: Find difference

$A_X - A_Y = 10880 - 10400 = 480$
Wait, but let's confirm: 0.002×20=0.04, so Y's interest is 10000×0.04=400, total Y=10400. X's interest: 8000×0.018×20=8000×0.36=2880, total X=10880. So difference is 480.

Ah, yes! I had misread Y's rate as 2% instead of 0.2%. So the correct difference is 480.

Final Answer:

480

Step1: Compute Account X's value

$A_X = 8000 + (8000×0.018×20) = 10880$

Step2: Compute Account Y's value

$A_Y = 10000 + (10000×0.002×20) = 10400$

Step3: Calculate the difference

$10880 - 10400 = 480$

Answer:

2000