A perpetuity-immediate with annual payments is priced at X based on an annual effective interest rate of 10%. The amount of the first payment is 14,000. Each payment, from the second through the twentieth, is 4% larger than the previous payment. The 21st payment and each subsequent payment will be 1% larger than the previous payment.

Calculate X.

• 185,542
• 191,834
• 206,540
• 208,508
• 212,823

An annuity writer sells an annual perpetuity-immediate for 16,000. The first payment is 1,000 and the payments decrease by r% each year. The annual effective yield rate is 5.7%.

Calculate r.

• 0.52
• 0.55
• 0.62
• 0.73
• 0.91

A perpetuity makes payments every five years with a first payment of 2 to be paid five years from now. Each subsequent payment is 10 more than the previous payment. The annual effective interest rate is 9%.

Calculate the present value of the perpetuity.

• 34.47
• 35.80
• 36.33
• 37.12
• 38.18

Susan won the lottery today which will pay an annual perpetuity of X, with the first payment occurring five years from today. The perpetuity has a present value of 100,000 based on an annual effective interest rate of 1% for the first ten years and 5% for all years thereafter.

Calculate X.

• 4100
• 4224
• 4357
• 4401
• 5696

Greg buys a 20-year increasing annuity-immediate with annual payments. The first payment is 110 and each succeeding payment is equal to the previous payment plus X. The annuity is priced at 2000 based on an annual effective interest rate of 10%.

Calculate X.

• 16.64
• 17.45
• 19.19
• 21.00
• 22.68

At an annual effective interest rate of 5%, a 10-year annuity-immediate starting with an annual payment of 100 increases each year by 15% of the previous year's payment and has a present value of X.

Calculate X.

• 597
• 772
• 1040
• 1247
• 1484

You have the option of purchasing one of the following two annuities-immediate:

1. The first annuity makes annual payments of 1000 for 20 years.
2. The second annuity is a perpetuity that also has annual payments. The payment in each of the first 10 years is 600. Beginning in year 11, the payments increase to 1200, and remain at 1200 forever.

At an annual effective interest rate of i > 0 , both annuities have a present value of X.

• 8700
• 8750
• 8800
• 8850
• 8900

Calculate X.

At the end of each year for 60 years, Marilyn makes a deposit to a bank account that credits interest at an annual effective interest rate of i. She deposits 2 at the end of the first year, and each subsequent year her deposit increases by 2. At the end of 60 years, Marilyn uses the accumulated amount to purchase a 5-year annuity-immediate paying annually at the same annual interest rate of i, with a first payment of X and each subsequent payment increasing by 5%. Which of the following expressions represents a correct equation of value?

• [[math]]\quad \frac{2\left(s_{60}-60\right)}{i}=\frac{X\left(1-(1.05 v)^5\right)}{i-0.05}[[/math]]
• [[math]]\quad 2(I a)_{\overline{60}}=X v^{60}\left(1+1.05 v+\ldots+(1.05 v)^4\right)[[/math]]
• [[math]]\quad 2 \sum_{t=0}^{59} s_{\overline{60-t}}=X\left(v+1.05 v^2+\ldots+1.05^4 v^5\right)[[/math]]

• I only
• II only
• III only
• I, II, and III
• The correct answer is not given by (A), (B), (C), or (D).

On his 65th birthday, an investor withdrew an amount P from a fund of 1,000,000 and withdrew the same amount on each successive birthday. On the date of his 82nd birthday, the fund was again equal to 1,000,000 after the withdrawal.

The fund earns an annual effective interest rate of 10%.

Calculate P.

• 81,655
• 88,915
• 90,909
• 98,879
• 109,729

The first payment of a five-year annuity is due in five years in the amount of 1000. The subsequent four annual payments increase by 500 each year. The annual effective interest rate is i.

Determine which of the following formulas gives the present value of the annuity.

• [[math]]\quad v^6\left[500 a_{5 \mid i}+500(I a)_{5 \mid i}\right][[/math]]
• [[math]]\quad v^6\left[500 \ddot{a}_{\left.5\right|_i}+500(I \ddot{a})_{\left.5\right|_i}\right][[/math]]
• [[math]]v^5\left[500 a_{\left.5\right|_i}+500(I \ddot{a})_{\left.5\right|_i}\right][[/math]]
• [[math]]\quad v^5\left[500 \ddot{a}_{5 \mid i}+500(I \ddot{a})_{\left.5\right|_i}\right][[/math]]
• [[math]]\quad v^5\left[1000 \ddot{a}_{\left.5\right|_i}+500(I \ddot{a})_{5 \mid i}\right][[/math]]