Question

You are running a bank and a customer wants to borrow $2m from the bank starting in 207 days and ending in 321 days. You charge interest on an ACT/360 basis and will set the rate at 0.61% above fair. Interest rates are:

Days	Cont. Comp. Rates
207	3.28
321	3.93

What rate do you charge? Give your rate to 2 decimal places and enter 3.05% as 3.05.

Answer 1

Assuming the same interest calculating convention of ACT/360

Let the fair interest rate be r for a loan starting in 207 days and ending in 321 days i.e for 114 days

The fair interest rate r should be such that an amount invested for 207 days and subsequently at r gives the same amount as amount invested for 321 days

So, exp (0.0328*207/360)* exp(r*114/360) = exp (0.0393*321/360)

=> exp (0.0328*207/360+r*114/360) = exp (0.0393*321/360)

=> (0.0328*207/360+r*114/360) = (0.0393*321/360)

=> r*114/360 + 0.01886 =0.035043

=> r*114/360 = 0.016183

=> r = 0.051103 or 5.11%

So, the rate charged is 5.11%+0.61% =5.72% continuously compounded rate (Enter 5.72)

(NOTE: In case interest convention of ACT/365 is used to calculate fair value of r , it still comes as 5.11% , but since the interest rate charged is on ACT/360 basis, on ACT/360 basis, it will be 5.18% so, the rate charged will be 5.79%)