Problem 2.1 Money in a bank account earns 7% simple interest per year.

(a) What is the effective rate of interest for the time interval [3,4]?

(b) What is the effective rate of discount for the time interval [3,4]?

Problem 2.2 At time t = 0, $1 is deposited into Fund A and Fund B. Fund A accumulates at a force of interest (t) = t 2/k for some k > 0. Fund B accumulates at a nominal annual rate of discount of 8% convertible semi-annually. At time t = 5 the accumulation in both funds is the same. Find k.

Problem 2.3 Investor A deposits $3,000 into a fund earning a constant force of interest of . In 6 years the fund will accumulate to $4,000. Investor B deposits $2,500 into a fund earning an effective annual rate of discount d. The accumulated values of the two funds are equal four years from today. Calculate d.

Problem 2.4 Money is deposited in a bank account. For the first 4 years the account earns a nominal annual rate of 8% converted monthly. For the next 6 years the balance accumulates at a force of interest of 6%. For this 10 year period, what is the equivalent nominal annual discount rate, convertible quarterly?

Problem 2.5 A business permits its customers to pay with a credit card or to receive a percentage discount r for paying cash. For credit card purchases, the business receives 95% of the purchase price 1/2-month later. At an effective annual rate of 12%, the two payment methods are equivalent. Find r.