Carol Miller went to Europe and forgot to pay her $750 mortgage payment on her New Hampshire ski house. For her 45 days overdue on her payment, the bank charged her a penalty of $16. (assume 360 days).
What was the rate of interest charged by the bank? (Do not round intermediate calculations. Round your answer to the nearest hundredth percent. Omit the "%" sign in your response.)
Interest charged 17.06
Explanation:
$16
R =
= 17.07%
$750 × 45
360
To find the rate of interest charged by the bank, we can use the formula for simple interest:
Simple Interest = Principal * Rate * Time
In this case, the principal is the $750 mortgage payment, and the time is 45 days (or 45/360 of a year). We need to find the rate.
Let's plug in the values and solve for the rate:
$16 = $750 * Rate * (45/360)
First, let's simplify the equation by canceling out common terms:
16 = 750 * Rate * (1/8)
To isolate the rate, divide both sides of the equation by (750 * (1/8)):
16 / (750 * (1/8)) = Rate
Now, calculate the right side of the equation:
16 / (750 * (1/8)) = Rate
16 / (750/8) = Rate
16 * (8/750) = Rate
(16 * 8) / 750 = Rate
128 / 750 = Rate
0.17066666667 = Rate
Now, round the rate to the nearest hundredth percent:
Rate ≈ 0.1707
Convert the decimal to percentage notation by multiplying by 100:
Rate ≈ 0.1707 * 100 = 17.07%
Therefore, the rate of interest charged by the bank is approximately 17.07%.