An interest rate is a rate which is charged or paid for the use of money. Another definition is annual cost of credit or debt-capital computed as the percentage ratio of interest to the principal.
a) A Bank offers an annual interest rate of 8% with quarterly compounding. What is the continuous compounding rate or the annual compounding rate?
The continuous compounding rate is
4 * ln(1+8%/4) ≈ 7.921%
The annual compounding rate is
(1 + 8%/4)^4 - 1 ≈ 8.243%
b) What is the meaning of LIBOR and of LIBID? Which of these interest rates is lower?
LIBOR is the interest rate at which the London banks are willing to offer funds in the inter-bank market. LIBOR is the average of rates which five major London banks are willing to lend $10 million for a period of three or six months, and is the benchmark rate for setting interest rates for adjustable-rate loans and financial instruments. LIBID is the interest rate at which London banks are willing to borrow from one another in the inter-bank market. LIBID is the average of rates which five major London banks willing to bid for a $10 million deposit for a period of three or six months. Since nobody would be willing to buy something at a higher price than to sell it, LIBID is lower than LIBOR.
c) An investor receives 1,080 USD after one year if he invests 1,000 USD today. What is the return in % p.a.
i. at annual compounding? 1*((1080/1000)^(1/1)-1)
ii. at semi-annual compounding? 2*((1080/1000)^(1/2)-1)
iii. at monthly compounding? 12*((1080/1000)^(1/12)-1)
iv. at continuous compounding? LN(1080/1000)
Interest rate parity is explained here.