When Sara Whitehorse changed jobs, she rolled over the $54,725 in her retirement account into two simple interest accounts. On one account, the annual simple interest rate is 8.75%, and on the second account, the annual simple interest is 5%. How much must be invested in each account if the two accounts earned the same amount of annual interest?
(x at 8.75% and y at 5%.)
A) x = $19,900; y = $34,825
B) x = $19,910; y = $34,815
C) x = $34,825; y = $19,900
D) x = $20,000; y = $34,925
E) x = $20,001; y = $34,724

Question

Quizplus · Accepted Answer

Let x be the amount invested in the account with 8.75% simple interest rate, and y be the amount invested in the account with 5% simple interest rate. Then we have the following system of equations:

x + y = 54725
0.0875x = 0.05y

Solving for y in the second equation, we get:

y = 1.75x

Substituting into the first equation, we get:

x + 1.75x = 54725
2.75x = 54725
x = 19900

Therefore, y = 1.75x = 34825. So the amounts invested in the two accounts are $19,900 and $34,825, respectively. Thus, the answer is (A).

When Sara Whitehorse Changed Jobs, She Rolled Over the $54,725