Question

10.) tara long borrowed $10,000 for 180 days. she paid exact interest at an annual rate of 12%. what was the total interest? what was the total amount she had to repay?
11.) bill rich signed a 180 - day note for $1,250. he repaid the loan when due with interest at an annual rate of 12% using the banker’s year. how much interest did he pay? what was the total amount he paid back to the bank?

Explanation:

Problem 10

Step1: Recall the simple interest formula

The formula for simple interest is $I = P \times r \times t$, where $I$ is the interest, $P$ is the principal amount, $r$ is the annual interest rate (in decimal), and $t$ is the time in years. For exact interest, the time $t$ is calculated as the number of days divided by 365. Here, $P = \$10,000$, $r = 12\% = 0.12$, and $t=\frac{180}{365}$.

Step2: Calculate the interest

Substitute the values into the formula: $I = 10000\times0.12\times\frac{180}{365}$. First, calculate $10000\times0.12 = 1200$. Then, $1200\times\frac{180}{365}=\frac{1200\times180}{365}=\frac{216000}{365}\approx\$591.78$.

Step3: Calculate the total amount to repay

The total amount $A$ is the principal plus the interest, so $A = P + I$. Substitute $P = 10000$ and $I\approx591.78$: $A = 10000 + 591.78=\$10591.78$.

Step1: Recall the simple interest formula for banker's year

For the banker's year, the time $t$ is calculated as the number of days divided by 360. The formula for simple interest is $I = P \times r \times t$, where $P = \$1,250$, $r = 12\% = 0.12$, and $t=\frac{180}{360}$.

Step2: Calculate the interest

Substitute the values into the formula: $I = 1250\times0.12\times\frac{180}{360}$. First, calculate $1250\times0.12 = 150$. Then, $150\times\frac{180}{360}=150\times0.5 = \$75$.

Step3: Calculate the total amount to pay back

The total amount $A$ is the principal plus the interest, so $A = P + I$. Substitute $P = 1250$ and $I = 75$: $A = 1250 + 75=\$1325$.

Answer:

Total interest: $\approx\$591.78$; Total amount to repay: $\approx\$10591.78$

Problem 11