A perpetuity-immediate pays 20 for 10 years, decreases by 1 per year for 19 years, and then pays 1 per year thereafter. At an annual effective interest rate of 6%, the present value is equal to X.

Calculate X.

• 208
• 213
• 218
• 223
• 228

Two immediate annuities have the following characteristics:

X: [math]\quad[/math] Pays [math]1 / m, m[/math] times per year, for 10 years

Y: [math]\quad[/math] Pays [math]P[/math] at the end of years 2, 4, 6, 8, and 10

You are given

1. The accumulated value at time 1 of [math]1 / m[/math] paid at times [math]1 / m, 2 / m, \ldots, 1[/math] is 1.0331 .
2. [math]\quad s_2=2.075[/math].
3. The present value of [math]X[/math] equals the present value of [math]Y[/math].

Calculate [math]P[/math].

• 1.94
• 2.01
• 2.03
• 2.07
• 2.14

At the beginning of each year, a payment of 5000 is invested in a fund. The payments earn an annual effective interest rate of 8%. At the end of each year, the interest is reinvested in the fund at an annual effective interest rate of 5%. The amount in the fund at the end of ten years, immediately prior to the 11 th annual payment, is X.

Calculate X to the nearest 100.

• 67,600
• 70,300
• 75,700
• 78,200
• 80,700

A perpetuity pays 1 at the beginning of each three-month period. Another perpetuity pays X at the beginning of each four-year period. Using an annual effective interest rate of i, each perpetuity has a present value of 300.

Calculate X.

• 15.41
• 15.61
• 15.91
• 16.21
• 16.41

An annual perpetuity pays 1 one year from now. Payments will then increase by 4% per year for 5 years and 8% per year thereafter. Calculate the present value of this perpetuity at an annual effective interest rate of 12%.

• 21.13
• 23.51
• 25.95
• 28.87
• 31.23

Susan receives annual payments from a 20-year annuity-immediate. The payment in year 1 is 100 and in each succeeding year the payment is 90% of the prior year’s payment. Upon receipt of each payment, Susan invests the payment in a savings account earning interest at a 3% annual effective rate. Calculate the balance in the savings account immediately after Susan invests the last annuity payment.

• 696
• 717
• 739
• 1296
• 1335

An annuity-immediate provides annual payments of 10 for 20 years. Immediately following the 11th payment, the annuity is exchanged for a perpetuity-immediate of equal value with semi- annual payments. The present values at the time of the exchange are based on an annual effective interest rate of 6%. The first payment of the perpetuity is K and each subsequent payment is 0.5% larger than the previous payment.

Calculate K.

• 1.53
• 1.67
• 2.37
• 3.42
• 3.74

An insurance company purchases a perpetuity-due at an annual effective yield rate of 12.5% for 9450. The perpetuity provides annual payments according to the repeating three-year pattern 100, X, 100, 100, X, 100, 100, X, 100, ... .

Calculate X.

• 2950
• 2963
• 3321
• 3344
• 3359

A perpetuity-due with annual payments is priced at X based on an annual effective interest rate of 7%. The amount of the first payment is 350. Each payment, from the second through the thirtieth, is 3% larger than the previous payment. Starting with the 31st payment, each payment is equal to the 30th payment.

Calculate X.

• 7508
• 7855
• 7925
• 7971
• 8033

A perpetuity-immediate with annual payments consists of ten level payments of k, followed by a series of increasing payments. Beginning with the eleventh payment, each payment is 200 larger than the preceding payment. Based on an annual effective interest rate of 5.2%, the present value of the perpetuity is 50,000.

Calculate k.

• 34
• 86
• 163
• 283
• 409