A payment of 7 is deposited into an account at the end of each year for 45 years. The account earns an annual effective interest rate of i. Immediately after the 45th deposit of 7, the account has accumulated to X, which is used to purchase a perpetuity-immediate. At an annual effective interest rate of 1.2i, the perpetuity will make annual payments of 75.60.

Calculate X.

• 1050
• 1120
• 1200
• 1260
• 1340

An n-year annuity, with a payment of 1 at the end of each year, has a present value of 5.5554 at an annual nominal interest rate, convertible m times per year. Also:

1. j is the effective rate of interest per interest conversion period, and
2. [math](1+j)^m = 1.0614 [/math]

Calculate n.

• 7
• 8
• 9
• 10
• There is insufficient information to calculate n

An investor wants to accumulate 150,000 to purchase a business in ten years. The investor deposits 14,000 into an account at the beginning of each of years one through five. The investor deposits an additional amount X at the beginning of years four and five to meet this goal. The account earns interest at an annual effective rate of 8%.

Calculate X.

• 2,113
• 2,592
• 5,958
• 9,595
• 11,574

Today’s deposit of 9550 earns an annual effective interest rate of i for five years. At the end of the fifth year, the entire accumulated balance is reinvested into a 20-year annuity-due. The annuity-due has level annual payments of 756.97 at an annual effective interest rate of 4%.

Calculate i.

• 1.5%
• 2.3%
• 7.7%
• 12.0%
• 19.7%

An actuary invests 1000 at the end of each year for 30 years. The investments will earn interest at a 4% annual effective interest rate and, at the end of each year, the interest will be reinvested at a 3% annual effective interest rate.

Calculate the accumulated value of the investment at the end of the 30-year period.

• 51,625
• 53,434
• 55,260
• 58,437
• 58,938

An annuity writer sells an annual perpetuity-due, with a first payment of 3000. The payments increase by 7% annually. The purchase price, P, of the perpetuity is based on a 12% annual force of interest.

Calculate P

• 41,096
• 52,177
• 58,829
• 60,000
• 67,200

An investor opens a savings account with no initial deposit that pays a constant 4.5% annual force of interest. The investor deposits 700 at the end of every six-month period for 20 years. The account balance immediately after the last deposit is X.

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

• [[math]]\quad \sum_{n=0}^{39} 700 e^{0.0225 n}=X e^{-0.9}[[/math]]
• [[math]]\quad \sum_{n=0}^{39} 700 e^{-0.0225 n}=X e^{0.9}[[/math]]
• [[math]]\quad \sum_{n=0}^{39} 700 e^{-0.0225 n}=X e^{-0.9}[[/math]]
• [[math]]\quad \sum_{n=0}^{39} 700 e^{0.0225 n}=X e^{0.9}[[/math]]
• [[math]]\quad \sum_{n=1}^{40} 700 e^{-0.0225 n}=X e^{-0.9}[[/math]]

You are given the following information regarding two annuities with annual payments:

1. Annuity X is a 20-payment annuity-immediate which provides an initial payment of 2500 and each subsequent payment is 5% larger than the preceding payment.
2. Annuity Y is a 30-payment annuity-due which provides an initial payment of k and each subsequent payment is 4% larger than the preceding payment.

Using an annual effective interest rate of 4%, Annuity X and Annuity Y have the same present value.

Calculate k.

• 1,758
• 1,828
• 1,901
• 2,078
• 2,262

An individual is to receive 1,000,000 today and 1,000,000 five years from today. These payments are to be converted to an increasing annual perpetuity, with the first payment, X, paid today and each succeeding payment 1000 more than the previous payment. At an annual effective interest rate of 4%, the present value of the two payments is equal to the present value of the perpetuity.

Calculate X.

• 45,074
• 47,877
• 51,923
• 55,000
• 66,795

An annuity has payments of 1000 at the beginning of every three months for six years. Another annuity has payments of X at the end of the first, third, and fifth years. At an annual effective rate of 8%, the present values of the two annuities are equal.

Calculate X.

• 7931
• 7981
• 8033
• 8085
• 8137