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1.1

1. Sally has two IRAs. IRA 1 earns interest at 8% effective annually and IRA 2 earns interest at 10% effective annually. She has not made any contributions since January 1, 1985, when the amount in IRA 1 was twice the amount in IRA 2.The sum of the two accounts on January 1, 1993 was $75000. Determine how much was in IRA 2 on January 1, 1985? （Individual Retirement Account）

2. Suppose we are given that the effective rate of interest is 5% in the first year and 6% in the second year .We invest $1 at time 0. How much is in the fund at the end of two years?

3. An investor puts 100 into Fund X and 100 into Fund Y. Fund Y earns compound interest at the annual rate of j, and Fund X earns simple interest at the annual rate of 1.05j . At the end of 2 years, the amount in Fund Y is equal to the amount in Fund X. Calculate the amount in Fund Y at the end of 5 years?

4. Eric deposits X into a savings account at time 0, which pays interest at a nominal rate of i , compounded semiannually. Mike deposits 2X into a different savings account at time 0, which pays simple interest at an annual rate of i .Eric and Mike earn the same amount of interest during

the last 6 months of the 8th year. Calculate i.

5. John invests 1000 in a fund which earns interest during the first year at a nominal rate of K convertible quarterly. During the 2nd year the fund earns interest at a nominal discount rate of K convertible quarterly. At the end of the 2nd year, the fund has accumulated to 1173.54. Calculate K.

6. A deposit of X is made into a fund which pays an annual effective interest rate of 6% for 10 years. At the same time, X/2 is deposited into another fund which pays an annual effective rate of discount of d for 10 years. The amounts of interest earned over the 10 years are equal for both funds. Calculate d.

7. You are given: A(t)?Kt2?Lt?Mfor0?t?2

A(0)?100,A(1)?110,A(2)?136

Determine the force of interest at time t?

1. 28. At time 0, 100 is deposited into Fund X and also into Fund Y. Fund X accumulates at a force of interest

?t?0.5?1?t??2. Fund Y

accumulates at an annual effective interest rate of i . At the end of 9 years, the accumulated value of Fund X equals the accumulated value of Fund Y. Determine i .

1.2

1. At an effective annual interest rate of i,i?0, each of the following two sets of payments has present value K:

1) A payment of 121 immediately and another payment of 121 at the end of one year.

2) A payment of 144 at the end of two years and another payment of 144 at the end of three years. Calculate K.

2. You are given:

1) The sum of the present values of a payment of X at the end of 10 years and a payment of Y at the end of 20 years is equal to the present value of a payment of X+Y at the end of 15 years. 2) X+Y=100

3) i?5%. Calculate X.

3.A customer is offered an investment where interest is calculated

?0.02t0?t?3according to the following force of interest :?t??

t?3?0.045The customer invests 1000 at time 0. What nominal rate of interest , compounded quarterly, is earned over the first four-year period?

4. Payments of 300,500 and 700 are made at the end of years five, six