^[1] Complete the following table, assuming an interest rate of 10% compounded quarterly.

 

^[2] Make a table with the same headings as previous, but for a loan of $12,000 for 5 months at 15% compounded monthly.

 

^[3] Write the following nominal rates in the “j_m” notation and find the corresponding periodic rates, i (include the period with these). The first line is completed as an example.

 

^[4] Write each of the following rates as nominal rates and complete the table.

 

^[5] Complete the following table, using the compound interest formula to calculate the future value of each loan.

^[6] Government compound-interest savings bonds have the interest compounded every year. Suppose that a $1,000 bond paid interest at 8.5% compounded annually and was kept for three years. Find the value (Future Value) of the bond at the end of the three years by:

(a) Showing the interest and balance each year.

(b) Using the compound-interest formula to get FV at the end of two years.

 

^[7] A loan of $24,000 for two years is to carry interest at 14% compounded semi-annually. Use the compound interest formula to find the value of the loan at the end of two years.

 

^[8] A “junk” bond was supposed to pay interest at 25% paid annually. Unfortunately, no payments were made for the last seven years, so the interest was allowed to compound at 25% compounded annually.

(a) Find the value at the end of each of the seven years for a bond with a principal of $1,000 at the start.

(b) Also find the value the loan would have had at the end of each year if the interest had been simple interest at 25% annually. Note the difference caused by compounding.

 

^[9] Find the present values of each of the amounts below, filling in the rest of the table when you do so.

PV	Interest Rate	Length	n	FV
?	6.5% compounded semi-annually	2 years	?	$11,364.76
?	16% compounded monthly	3.5 years	?	$25,000.00
?	I0% compounded quarterly	1 year	?	$30,000.00

Check your last result by assuming the PV was invested for one year in an account paying 10% compounded quarterly and adding on the interest each period as in Problem 1.

 

^[10] According to the terms of his uncle’s will, Tom Jones is to receive $50,000 2.5 years from now. Tom would like to borrow as much as he can now and pay it off with his inheritance. Use the compound-interest formula to find out how much he can borrow if the interest rate is as follows:

(a) 10% compounded monthly.

(b) 9% compounded monthly.

(c) 8% compounded monthly.

 

^[11] Ann Lee has a lease on a government property which must be paid by a lump sum of $6,000 every year. The next payment is due in 10 months from now, and Ann plans to invest enough money in an account at her bank so that the amount in the account in 10 months will cover the $6,000 payment. If the interest rate is 8.5% compounded monthly, how much should she place in the account?

 

^[12] Ajax Company is borrowing $100,000 now and has agreed to pay 11% compounded annually on the outstanding balance at all times. Ajax plans to pay $30,000 at the end of the first year of the loan and $35,000 at the end of the second year. The remaining debt is to be completely paid off by a single payment at the end of the third year. Draw a cash-flow diagram and find the amount that should be paid at the end of the third year by:

(a) Finding the interest and balance due at the end of each year.

(b) Using an equation of value at a focal date (e.g., at year 3).

 

^[13] AC Holdings has taken over a company with a debt that was to be paid by a payment of $85,000 one year from now. Instead, AC has agreed with the holder of the debt to pay it off early and be allowed 12% compounded quarterly for early payment. It plans to pay $40,000 now and the rest in six months.

(a) Draw a cash-flow diagram and find the amount that should be paid in 6 months.

(b) Repeat (a) but assume the payments now and in 6 months are to be equal in size.

 

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