Question

Negotiating the Rate.  A sovereign borrower is considering a 100 million loan for a 4​-year

maturity. It will be an amortizing​ loan, meaning that the interest and principal payments will​ total, annually, to a constant amount over the maturity of the loan. There​ is, however, a debate over the appropriate interest rate. The borrower believes the appropriate rate for its current credit standing in the market today is 10​%, but a number of international banks with which it is negotiating are arguing that is most likely 14%, at the minimum 10​%. What impact do these different interest rates have on the prospective annual​ payments?

1. The annual payment, if the interest was set at 10%?
2. The annual payment, if the interest was set at 14%
3. The difference in annual payment?

Answer 1

Given Loan Period Rate 1 Rate 2 100 Million 4 Years 10% 14% Solution We know that formula for annual payment is Annual Payment = Loan Amount PVAF where PVAF = (1+r)^n-1 rX(1+r)^n = Rate = Period Part A: The annual payment, if interest rate was set at 10% Annual Payment 100 3.170 31.55 Hence, annual Payment is 31.55 Miilion Part B: The annual payment, if interest rate was set at 14% Annual Payment 100 2.914 34.32 Hence, annual Payment is 34.32 Miilion Part C: Difference in annual payment Hence, difference in annual payment = Annual payment at rate 14% - annual payment at rate 10% = 34.32 -31.55 = 2.77 Million.