Discounted loan in financial math

[vincentmls]

Problem 3 (Required, 25 marks)
A bank has offered a discounted loan. It is given that the loan charges interest at an
annual nominal discount rate ?(?) convertible ?-thly (where ? is positive integer).
 Borrower A has entered into ?-year discounted loan and borrow $5000. It is
given that the actual amount that borrower receives now is $4630.
Recently, another borrower B has entered into 2?-year discounted loan and borrow
$10000.
Questions
(a) Calculate the amount of interest charged by the bank in borrower B’s loan.
(b) Suppose that the borrower B negotiates with the bank and agree that the
borrower can pay the interest (together with the principal $10000) after 2? year.
To do so, the bank decides to charge interest at an annual nominal discount rate
2?(?) convertible 2?-thly. Calculate the total repayment amount paid by the
borrower after 2? years.
(Hint: It is impossible to find the values of all unknowns ?(?), ? and ?. To solve this
problem, you just need the value of one unknown (combination of ?(?), ? and ?).)

 

[tkhunny]

That's a lovely problem. What can you show us?

First off, let's see if we have an idea what "discount" is.

If you enter into a one-year loan at 9% discount, compounded annually, the loan originator will provide how much to you, the borrower, at the beginning of the loan?