# Ethan has \$9079 in his retirement account, and Kurt has \$9259 in his. Ethan is adding \$19per day, wh

Discussion in 'Calculator Requests' started by math_celebrity, Mar 25, 2019.

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Ethan has \$9079 in his retirement account, and Kurt has \$9259 in his. Ethan is adding \$19per day, whereas Kurt is contributing \$1 per day. Eventually, the two accounts will contain the same amount. What balance will each account have? How long will that take?

Set up account equations A(d) where d is the number of days since time 0 for each account.
Ethan A(d): 9079 + 19d
Kurt A(d): 9259 + d

The problems asks for when they are equal, and how much money they have in them. So set each account equation equal to each other:
9079 + 19d = 9259 + d

Typing this equation into our search engine, we get d = 10.
So in 10 days, both accounts will have equal amounts in them.

Now, pick one of the account equations, either Ethan or Kurt, and plug in d = 10. Let's choose Kurt's since we have a simpler equation:
A(10) = 9259 + 10
A(10) = \$9,269

After 10 days, both accounts have \$9,269 in them.