Question

Harper deposited $110 into a savings account that earns 3.5% interest a year. The function (R)t models the amount of money Raymond has in his savings account as a function of time (t) in years. R(t)=110(1.025)^t How much more money will Harper have in his savings account than Raymond after two years? A: $2.26 B: $7.83 C: $5.57 D: $3.37

Answer 1

A. $2.26

Explanation:

An equation for Harper's balance can be written similar to the one written for Raymond's balance. It will be ...

H(t) = 110(1.035)^t

For t = 2, the two balances will be ...

H(2) = 110(1.035^2) = 117.83

R(2) = 110(1.025^2) = 115.57

The difference is ...

$117.83 -115.57 = $2.26

Harper's account will have $2.26 more.

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As a quick estimate or sanity check, you can see that Harper's interest rate is 1% more than Raymond's. So, in 2 years, he will earn a little more than 2% more on his investment than Raymond earns. 2% of $110 is $2.20, so the difference can be expected to be slightly more than this.