Question

Joanne and ed greenwood built a new barn with an attached arena. to finance the loan, they paid $1,307 interest on $45,000 at 4.0%. what was the time, using exact interest? (do not round intermediate calculations. round up your answer to the nearest day.) time

Answer 1

To find the time using exact interest, use the formula I = PRT, where I is the interest, P is the principal, R is the interest rate per year, and T is the time in years. In this case, the time is approximately 1 year.

Step-by-step explanation:

To find the time using exact interest, we can use the formula for simple interest: I = PRT, where I is the interest, P is the principal (loan amount), R is the interest rate per year, and T is the time in years.

In this case, the interest is $1,307, the principal is $45,000, and the interest rate is 4.0% (or 0.04 as a decimal). Plugging these values into the formula, we get:

• $1,307 = $45,000 * 0.04 * T

Now, we can solve for T:

• T = $1,307 / ($45,000 * 0.04)

Calculating this, we find that T is approximately 0.7269 years. Rounded up to the nearest day, this is 1 year.

Answer 2

Answer: The loan was taken for 265 days.

We arrive at the answer as follows:

First we find the ratio of interest paid to the total loan amount to determine the interest rate:

Interest paid = $1,307

Loan Amount = $45,000

`(Int paid)/(Loan amount) = (1307)/(45000) = 0.029044444`

Since the interest rate calculated above is less than the annual interest rate at 4%, we conclude that the loan taken was for a period of less than one year.

We can determine the period for which the loan was taken as follows:

Let 'x' be the time for which the loan was taken.

We need to solve for x in the proportion below

0.04 : 365 :: 0.029044444:x

Solving we get,

`(0.04)/(365) = (0.029044444)/(x)`

`x = (0.029044444 * 365)/(0.04)`

`x = 265.0305556`