Question

1. - / 1 points use the ordinary interest method to compute the time (in days) for the loan. round your answer up to the next highest day when necessary. principal: $7,600; rate (%): 10.4; time: \boxed{} days; interest: $223

Explanation:

Step1: Recall ordinary interest formula

The ordinary interest formula is $I = P \times r \times \frac{t}{360}$, where $I$ is interest, $P$ is principal, $r$ is annual interest rate (decimal), and $t$ is time in days. Rearrange to solve for $t$:
$$t = \frac{I \times 360}{P \times r}$$

Step2: Convert rate to decimal

Convert 10.4% to decimal:
$r = \frac{10.4}{100} = 0.104$

Step3: Substitute values into formula

Plug in $I=223$, $P=7600$, $r=0.104$:
$$t = \frac{223 \times 360}{7600 \times 0.104}$$

Step4: Calculate numerator and denominator

Compute numerator: $223 \times 360 = 80280$
Compute denominator: $7600 \times 0.104 = 790.4$

Step5: Solve for t and round up

$$t = \frac{80280}{790.4} \approx 101.57$$
Round up to the next highest day.

Answer:

102 days