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

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

$\frac{Int paid}{Loan amount} = \frac{1307}{45000} = 0.029044444$

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,

$\frac{0.04}{365} = \frac{0.029044444}{x}$

$x = \frac{0.029044444 * 365}{0.04}$

$x = 265.0305556$