In: Accounting
This question illustrates what is known as discount
interest. Imagine you are discussing a loan with a somewhat
unscrupulous lender. You want to borrow $30,000 for one year. The
interest rate is 19.75 percent. You and the lender agree that the
interest on the loan will be .1975 × $30,000 = $5,925. So, the
lender deducts this interest amount from the loan up front and
gives you $24,075. In this case, we say that the discount is
$5,925.
What is the interest rate on this loan? (Do not round
intermediate calculations and round your answer to 2 decimal
places, e.g., 32.16.)
Interest rate
%
Interest rate on this loan will equal to the rate at which present value of loan repayment amount is equal to borrowed amount (i.e net of discount)
Amount borrowed = Amount to be repaid after 1 year*PVF(i%, 1) (Where i% = interest rate on loan)
$24,075 = $30,000*PVF(i%, 1)
PVF(i%, 1) = $24,075/$30,000 = 0.8025
1/(1+i%) = 0.8025
(1+i%) = 1/0.8025
(1+i%) = 1.2461
i% = 1.2461-1 = 0.2461 or 24.61%
Therefore the interest rate on this loan is 24.61%.