An investor decides to purchase a five-year annuity with an annual nominal interest rate of 12% convertible monthly for a price of X.

Under the terms of the annuity, the investor is to receive 2 at the end of the first month. The payments increase by 2 each month thereafter.

Calculate X.

• 2015
• 2386
• 2475
• 2500
• 2524

A perpetuity-due with semi-annual payments consists of two level payments of 300, followed by a series of increasing payments. Beginning with the third payment, each payment is 200 larger than the preceding payment.

Using an annual effective interest rate of i, the present value of the perpetuity is 475,000.

Calculate i.

• 4.05%
• 4.09%
• 4.13%
• 4.17%
• 4.21%

At an annual effective interest rate of 6%, the present value of a perpetuity immediate with successive annual payments of 6, 8, 10, 12, ..., is equal to X.

Calculate X.

• 100
• 656
• 695
• 1767
• 2222

A perpetuity-due with annual payments consists of ten level payments of X followed by a series of increasing payments. Beginning with the eleventh payment, each payment is 1.5% larger than the preceding payment.

Using an annual effective interest rate of 5%, the present value of the perpetuity is 45,000.

Calculate X.

• 1,679
• 1,696
• 1,737
• 1,763
• 1,781

A family purchases a perpetuity-immediate that provides annual payments that decrease by 0.4% each year. The price of the perpetuity is 10,000 at an annual force of interest of 0.06.

Calculate the amount of the perpetuity’s first payment.

• 604
• 620
• 640
• 658
• 678

A 20-year arithmetically increasing annuity-due sells for 600,000 and provides annual payments. The first payment is X, and each payment thereafter is X more than the previous payment. A 25-year arithmetically increasing annuity-due provides annual payments. The first payment is X, and each payment thereafter is X more than the previous payment. The prices of the two annuities are calculated using a continuously compounded annual interest rate of 6%.

Calculate the price of the 25-year annuity.

• 667,026
• 668,707
• 750,000
• 779,336
• 782,712

An annuity provides level payments of 1000 every six months for a fixed period. Using an annual effective interest rate of i, the future value of this annuity at the time of the last payment is 19,549.25 and the present value of this annuity at the time of the first payment is 7,968.89.

Calculate i.

• 7.4%
• 8.5%
• 15.4%
• 17.0%
• 17.7%

Company Q invests X at the end of each year for 25 years at an annual effective interest rate of 9%. Company R invests 100 at the end of each year for 25 years at an annual effective interest rate of 9%, but, at the end of each year, the interest earned is reinvested at an annual effective interest rate of 8%. Immediately after the 25th payment, Company R’s total investment, including the reinvested interest, has the same value as Company Q’s investment.

Calculate X.

• 91.22
• 91.93
• 92.67
• 93.41
• 94.03

The present value of a perpetuity-due with payments of X at the beginning of each 3-year period with an annual effective interest rate of 7% is 735.

Calculate X.

• 135
• 138
• 141
• 144
• 147

The present value of a perpetuity-immediate with a first payment of P and successive annual increases of 9 at an annual effective interest rate of 6% is 2600.

Calculate P.

• 5.50
• 6.00
• 6.50
• 7.00
• 7.50