Two-Part Analysis - Quantitative
A bank has two options for 12 month certificates of deposit (CDs). Option A has an annual interest rate of 3% and a maximum deposit of $5,000. Option B has an annual interest rate of 2.5% and an unlimited deposit amount.
Alice and Jeremy invested in these CDs. Both put the maximum amount in Option A and then additional money in Option B. Alice made twice as much in total interest as Jeremy, and she made $350 more than Jeremy in interest from the Option B CD.
Select the amount of money invested in Option B by Alice, and select the amount of money invested in total by Jeremy. Make only two selections, one in each column.
If you did use algebra to get the exact answers, your work could look something like this, using J as the amount of interest Jeremy made from the Option B CD:
The total amount of interest Alice made is $$0.03(\$5{,}000)+J+\$350 = J+\$500$$. The total amount of interest Jeremy made is $$0.03(\$5{,}000)+J = J+\$150$$. Since Alice made twice as much interest as Jeremy, the following is true. $$J+\$500 = 2(J+\$150)$$ $$J+\$500=2J+\$300$$ $$J = \$200$$That means that Jeremy invested $8,000 ($200 divided by 2.5%) in the Option B CD.
Alice made $550 in interest from the Option B CD, so Alice invested $22,000 ($550 divided by 2.5%) in the Option B CD. Jeremy invested $13,000 in total ($5,000 in Option A and $8,000 in Option B).
Incorrect.
[[snippet]]Use the fact that Alice made $350 more than Jeremy in interest from the Option B CD to determine how much more Alice must have invested than Jeremy in the Option B CD.
If x is the amount Alice invests in the Option B CD, and y is the amount Jeremy invests in the Option B CD, then $$0.025x-0.025y = \$350$$.
Use the difference between x and y to determine the difference between the two answer values.
Incorrect.
[[snippet]]$14,000 is the difference between the amounts that Alice and Jeremy put in the Option B CD.
That's right!
That's right!
While you could algebraically find the exact values for each column, you can quickly find the difference between the two values using only the second piece of information given.
Use the fact that Alice made $350 more than Jeremy in interest from the Option B CD to determine how much more Alice must have invested than Jeremy in the Option B CD.
If x is the amount Alice invests in the Option B CD, and y is the amount Jeremy invests in the Option B CD, then the following is true.
$$0.025x-0.025y = \$350$$ _(Multiply both sides by 40.)_ $$x-y = \$14{,}000$$Since Jeremy also invested $5,000 in Option A, the amount Alice invests in the Option B CD will be $9,000 greater than the amount that Jeremy invests in total. That means that the value in the first column should be $9,000 greater than the value in the second column. The only values that match that difference are $22,000 and $13,000.
