Question

Linda Davis agreed to lend money to Alex Luciano at a special interest rate of ​9% per​ year, on the condition that he borrow enough that he would pay her ​$400 in interest over a ​-year period. What was the minimum amount Alex could​ borrow?

Answer 1

9514 1404 393

Answer:

$4444.44

Explanation:

The amount of interest on a given principal is found by ...

I = Prt . . . . principal P earning annual rate r for t years.

We want ...

400 = P×0.09×1

P = 400/0.09 ≈ 4444.44

Alex needs to borrow $4444.44.

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Additional comment

For exactly $400 in interest, the amount is not an integral number of cents, so some rounding of interest or loan amount must occur. In that case, the minimum to borrow is that which will give a calculated interest of at least $399.995. That amount is $399.994/0.09 ≈ $4444.3888.... ≈ $4444.39. Alex can borrow a minimum of $4444.39 and still have to pay $400 in interest.