Ezercise 2.31. You are a representative of a financial company. The company can
ID: 2414977 • Letter: E
Question
Ezercise 2.31. You are a representative of a financial company. The company can borrow and lend through an ideal bank having constant spot rate function R (T) R 5% for all T 0 A client (who does not have access to this bank) wants to borrow $100,000 for the period of one year. The amount $100,000 and the time one year will be called, respectively, the principal and the maturity of the loan. The client will readily accept any of the schemes below (1) In the first scheme all the interest and the principal will be paid at maturity The interest rate for this scheme is r11] 6%. (Notice that since the only payment takes place at t 1, there is no distinction between the nominal rate and the effective (2) In the second scheme there will be equal monthly interest payments (12 pay- ments in total plus payment of the principal at maturity. The nominal interest rate for this scheme is r2 12 6% (3) In the third scheme the loan will be amortized or repayed by equal monthly payments (12 payments in total). The nominal interest rate for this scheme is You naturally want to maximize the profit of the financial company. Which type of loan will you sell to the client? What will the time-0 valuee of your profit be?Explanation / Answer
1- future value = pv(1+r)^n = fv = 100000(1.06)^1 = 106000
2- 500*12 + 100000 = 106000
3- by applying excel formula =PMT(0.5%,12,100000,0,0) = 8606.64
monthly installment = 8606.64*12 = 103272
in the above three option i would prefer 2nd option because earning in option 1 and 2 is same but early payments are started in option 2 in the form of 500 of interest monthly and pricipal amount at the maturity.
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