Question

Marty Not is going to borrow $14,700 for 60 days and pay $143 in interest What is the annual rate of interest if the loan is discounted? (Use 365 days in a year. Do not round intermediate calculations. Round the final answer to 2 decimal places.) Annual rate of interest

Answer 1

We have:

Loan Amount : $14,700

Interest Amount : $143

Loan Tenure : 60 days

Number of days in a year : 365 days

Since the loan is discounted, it means that the bank will deduct the interest from the principal and give the rest of the amount to Marty Nor. At the end of 60 days, Marty Not will have to repay the principal.

This means Morty Nor will get: Loan amount received = (Amount borrowed - Interest)

Loan amount received = $14,700 - $143 = $14,557

Since Marty Nor gets $14,557 now, this amount is the Present Value or PV.

Marty Nor needs to repay $14,700 after 60 days, hence $14,700 is the Future Value or FV.

Since

FV = PV/(1+r),

(1+r) = FV/PV

Plugging in the values from above we get,

(1+r) = 14,700/14,557

(1+r) = 1.009823

r = 1.009823 -1

r = 0.009823

However, this is the interest rate for 60 days. We need to calculate the annual rate of interest.

We calculate that as:

Annual Interest Rate = (r/60) * 365

Annual Interest Rate = (0.009823/60) * 365

Annual Interest Rate = 0.059759 = 5.98%.

Answer 2

SOLUTION :

Interest rate for 60 days period = 143/14700 

Annual rate of interest 

= interest rate for the period * number of periods in a year

= 143/14700 * (365/60)

= 0.0592

= 5.92 % (ANSWER).

Answer 3

SOLUTION :

Loan is discounted.

So, amount received on taking loan = 14700 - 143 = 14557 ($)

Amount to be paid after 60 days = 14700 ($)

Interest rate for 60 days = 143/14557

So,

Annual interest rate 

= 143/14557 * (365/60) 

=  0.05976 

= 0.0598 approx.

= 5.98% (ANSWER)