Question

Your firm is considering two​ one-year loan options for a $ 541,000 loan. The first carries fees of 2.1% of the loan amount and charges interest of 4.2% of the loan amount. The other carries fees of 1.8 % of the loan amount and charges interest of 4.7 % of the loan amount.

a. What is the net amount of funds from each​ loan?

b. Based on the net amount of​ funds, what is the true interest rate of each​ loan?

a. What is the net amount of funds from each​ loan?

The net amount of funds for option 1 is ​$____. ​(Round to the nearest​ dollar.)

The net amount of funds for option 2 is ​$____. ​(Round to the nearest​ dollar.)

b. Based on the net amount of​ funds, what is the true interest rate of each​ loan?

The true interest for loan 1 will be ____%. ​(Round to three decimal​ places.)

The true interest for loan 2 will be ____%. ​(Round to three decimal​ places.)

Answer 1

Given :

Loan Amount : $541000

Option 1 : Fees 2.1% ; Interest 4.2%

Option 2 : Fees 1.8% ; Interest 4.7%

Option 1 :

Net Amount of Funds = Loan Amount ( 1 - Rate of Fees)

= $541000 ( 1 - 0.021)

= $ 529639

Interest Amount = Loan Amount * Rate of Interest

= $ 541000 * 0.042

= $22722

True Interest = Interest Amount / Net Amount of Funds

= 22722 / 529639

= 4.290%

Option 2 :

Net Amount of Funds = Loan Amount ( 1 - Rate of Fees)

= $541000 ( 1 - 0.018)

= $ 531262

Interest Amount = Loan Amount * Rate of Interest

= $ 541000 * 0.047

= $25427

True Interest = Interest Amount / Net Amount of Funds

= 25427 / 531262

= 4.786%

Final Answer :

The net amount of funds for option 1 is ​$ 529,639. ​(Round to the nearest​ dollar.)

The net amount of funds for option 2 is ​$ 531,262. ​(Round to the nearest​ dollar.)

The true interest for loan 1 will be 4.290 %. ​(Round to three decimal​ places.)

The true interest for loan 2 will be 4.786%. ​(Round to three decimal​ places.)