Question

1. A 6?-month ?$9000 Treasury bill with discount rate 8.671?% was sold in 2009. Find a. the price of the? T-bill, and b. the actual interest rate paid by the Treasury.

a. The price of the? T-bill is ?$

?(Round to the nearest dollar as? needed.)

2. Suppose that ?$30,000 is invested at 7?% interest. Find the amount of money in the account after 8 years if the interest is compounded annually.

If interest is compounded? annually, what is the amount of money after t = 8 ?years?

?(Do not round until the final answer. Then round to the nearest cent as? needed.)

3. Find the compound amount for the following deposit.

?$11,000 at 6?% compounded semi-annually for 6 years.

The compound amount after 6 years will be ?$

?(Round to the nearest? cent.)

4.A gift of ?$5000 to a city grew to ?$10?,000,000 in 200 years. At what interest rate compounded annually would this growth? occur?

The interest rate would be

?(Do not round until the final answer. Then round to the nearest hundredth as? needed.)

5.Find the APY corresponding to the following nominal rate.

3?% compounded quarterly

The APY is

?(Type an integer or a decimal. Round to the nearest hundredth as? needed.)

6.Find the APY corresponding to the following nominal rate.

4?% compounded quarterly

The APY is

?(Type an integer or a decimal. Round to the nearest hundredth as? needed.)

7.Find the future value of the following ordinary annuities. Payments are made and interest is compounded as given.

R=?$8000

5?% interest compounded annually for 20 years

What is the future value of the ordinary? annuity?

?(Round to the nearest? cent.)

8.Find the future value of the following ordinary annuities. Payments are made and interest is compounded as given. R=?$4000 10?% interest compounded annually for 5 years

What is the future value of the ordinary? annuity?

?(Round to the nearest? cent.)

9.Find the future value of a 13?-year annuity due with payments of ?$2,300 and an annual compound interest rate of 7.8?%.

The future value is ?$

?(Round to the nearest ?cent.)

10. Find the monthly house payments necessary to amortize a 10.8?% loan of ?$268,300 over 30 years.

The payment size is ?$

?(Round to the nearest? cent.)

11. Find the monthly house payments necessary to amortize an 8.4?% loan of ?$274,700 over 30 years.

The payment size is ?$

?(Round to the nearest? cent.)

12. Find the payment made by the ordinary annuity with the given present value. ?$89,382?; monthly payments for

17 ?years; interest rate is 4?%, compounded monthly

The payment is ?$

?(Simplify your answer. Round to the nearest cent as? needed.)

13. Find the payment made by the ordinary annuity with the given present value. $257,688?; quarterly payments for 20 ?years; interest rate is 9?%, compounded quarterly

The payment is ?$

?(Simplify your answer. Round to the nearest cent as? needed.)

14. Find the APY corresponding to the following nominal rate. 6?% compounded semiannually

The APY is

?(Type an integer or a decimal. Round to the nearest hundredth as? needed.)

15. Find the present value of the following future amount.

?$200,000 at 12?% compounded semiannually for 20 years

What is the present? value?

?(Round to the nearest? cent.)

Answer 1

1. Number of T-bill= 9000/100 = 90 bonds with face value of 100

Price = 180*8.671/360 = 4.3355

Price of T-bills = (100 -4.3355)*90 = $8,609.805

Actual interest rate = (9000-8609.805)/8609.805 = 0.0453 = 5.53%

2. Amount of money at t = 8 = 30000*(1+0.07)^8 = 51,545.59

3. Compounded amount = 11,000*(1+0.06/2)^12 = 15,683.37

4.Interest rate(annual) = (1 + (10,000,000-5,000)/5,000)^(1/200) -1

Interest rate (annual) = (1+1999)^(1/200) -1 =0.0387 = 3.87%

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