A perpetuity pays X at the end of the third year, 2X at the end of the sixth year, 3X at the end of the ninth year, etc. At a 6% annual effective interest rate, the present value of the perpetuity is 655.56.

Calculate X.

• 2
• 17
• 20
• 33
• 39

A perpetuity-immediate has monthly payments that increase by 5% every 12 payments. The initial 12 payments are 500 each. The present value of this perpetuity-immediate, using an annual effective interest rate of 8% is X.

Calculate X.

• 191,881
• 197,637
• 200,009
• 207,231
• 209,546

A level monthly contribution of X is required to purchase an annual perpetuity of 5000 that commences five years from today. The contributions are made at the end of each month for 60 months. The last contribution is made at the same time as the first payment from the perpetuity. The annual nominal interest rate is 12% compounded monthly.

Calculate X.

• 402
• 483
• 510
• 544
• 581

A payment of 55,400 made today returns payments of 10,000 at the beginning of each year for ten years. These payments are deposited into an account that earns interest at an annual effective rate of 6% payable at the end of each year. The interest is immediately reinvested at an annual effective interest rate of 4%. The original payment earns an annual effective yield rate of i over the ten-year period.

Calculate i

• 9.0%
• 9.5%
• 10.0%
• 10.5%
• 11.0%

An investor deposits 1000 at the beginning of each year for five years in a fund earning a 5% annual effective interest rate. The interest from this fund can be reinvested at a 4% annual effective interest rate.

Calculate the total accumulated value at the end of five years.

• 5058
• 5227
• 5436
• 5641
• 5791

The following deposits are made into a fund at the beginning of each year:

The fund earns an annual effective interest rate of 13%. At the end of the tenth year, the fund is used to purchase a perpetuity-immediate with semiannual payments of X. The perpetuity earns an annual effective interest rate of 12%.

Calculate X.

• 99
• 102
• 105
• 180
• 204

An investor deposits 225 into a bank at the beginning of each month for 20 years. The bank pays interest at an annual effective rate of 8%. At the end of 20 years, the investor uses the money in the bank to buy a 30-year annuity-due with annual payments of X. These annual payments are based on an annual effective interest rate of 7%.

Calculate X.

• 9,642
• 9,704
• 9,981
• 10,317
• 10,383

An investor deposits 50,000 into a new savings account, which earns an annual effective discount rate of 3.2%. The investor then withdraws an amount X at the end of every two-year period. The balance at the end of 12 years, just after the withdrawal, is 45,000.

Determine which of the following is an equation of value that can be used to solve for X.

• [[math]]\frac{45,000}{(1.032)^{12}}+X \sum_{k=1}^7 \frac{1}{(1.032)^{2(k-1)}}=50,000[[/math]]
• [[math]]\frac{45,000}{(1.032)^{12}}+X \sum_{k=1}^6 \frac{1}{(1.032)^{2 k}}=50,000[[/math]]
• [[math]]\quad 45,000(0.968)^{12}+X \sum_{k=1}^6(0.968)^{2 k}=50,000[[/math]]
• [[math]]\frac{45,000}{(1.032)^{12}}+X \sum_{k=1}^6(0.968)^{2 k}=50,000[[/math]]
• [[math]]\quad 45,000(0.968)^{12}+X \sum_{k=1}^6 \frac{1}{(1.032)^{2 k}}=50,000[[/math]]

Joe plans on going to Cal Tech. He will need to pay 4 payments of $50,000 when he goes there. In order to do this he will deposit x into an account every month that earns 8% interest convertible monthly for 7 years. He will take out the payments at the end of the last 4 years at the end of the year. After the last withdrawal the account will be exhausted. Calculate x.

• $2,084.95
• $2,016.80
• $2,019.78
• $3,534.01
• $1,999.60

Hardiek, Aaron (June 2010). "Study Questions for Actuarial Exam 2/FM". digitalcommons.calpoly.edu. Retrieved November 20, 2023.

Mat takes out a loan for a car for $35,000. He must make 16 annual payments of $4,000. For the first 7 years the interest rate is 8%, what is the annual effective interest rate for the last 9 years?

• .115
• .242
• .082
• .087
• .468

Hardiek, Aaron (June 2010). "Study Questions for Actuarial Exam 2/FM". digitalcommons.calpoly.edu. Retrieved November 20, 2023.