a) A savings plan requires you to make payments of 250 each at the end of every month for a year. The bank will then make six equal monthly payments to you, with its first payment due one month after the last payment you make to the bank. Compute the size of each monthly payment made by the bank, assuming a nominal interest rate of 4% p.a. payable monthly. (b) The situation is the same as in question (a): you make payments of 250 each at the end of every month for a year, and the rate is 4% p.a. payable monthly. However, now the bank will make equal annual payments to you in perpetuity, with the first payment due three years after the last payment you make to the bank. Compute the size of the annual payments. 2. (From the sample exam) A 20-year loan of 50,000 is repaid as follows. The borrower pays only interest on the loan, annually in arrear at a rate of 5.5% per annum. The borrower will take out a separate savings policy which involves making monthly payments in advance such that the proceeds will be sufficient to repay the loan at the end of its term. The payments into the savings policy accumulate at a rate of interest of 4% per annum effective. Compute the monthly payments into the savings account which ensures that it contains 50,000 after 20 years, and write down the equation of value for the effective rate of interest on the loan if it is repaid using this arrangement. 3. (From the CT1 exam, Sept '08) A bank offers two repayment alternatives for a loan that is to be repaid over ten years. The first requires the borrower to pay 1,200 per annum quarterly in advance and the second requires the borrower to make payments at an annual rate of 1,260 every second year in arrears. Determine which terms would provide the best deal for the borrower at a rate of interest of 4% per annum effective.

A borrower agrees to repay a loan of 3000 by 15 annual repayments of 500, the first repayment being due after five years. Find the annual yield for this transaction. 2. (From the sample exam) A loan of 50,000 is repaid by annual payments of 4000 in arrear over a period of 20 years. Write down the equation of value and use linear interpolation with trial values of i = 0.04 and i = 0.07 to approximate the effective rate of interest per annum.

On 15 November in each of the years 1964 to 1979 inclusive an investor deposited 500 in a special bank savings account. On 15 November 1983 the investor withdrew his savings. Given that over the entire period the bank used an annual interest rate of 7% for its special savings accounts, find the sum withdrawn by the investor. 2. A savings plan provides that in return for n annual premiums of X (payable annually in advance), an investor will receive m annual payments of Y , the first such payments being made one payments after payment of the last premium. (a) Show that the equation of value can be written as either Y an+m (X + Y )an = 0, or as (X + Y )sm Xsn+m = 0.

4. Use the Keynesian cross diagram, and illustrate how the AD would shift in each scenario. Indicate whether the economy would end up at a higher or lower equilibrium output. a. Households experience a decline in wealth as the value of housing drops when the housing bubble bursts. b. The nation's leaders tell consumers it is their patriotic duty to save the economy by consuming more, and consumers do so. This question is complete