felixliang1030
September 23rd 2010, 08:45 PM
FM Decal: UGBA 198
Model 2: Annuities and Perpetuities
1. A loan for 20000 must be repaid with 5 year end payments at an annual rate of 12%. What is the annual payment?
A) 5348 B) 5548 C) 5448 D) 5648 E) 5500
2. You have borrowed 15000 and agreed to repay the loan with 5 level payments of 4000, with the first payment occurring one year from today. What interest rate are you paying?
A) 10.1% B) 10.23% C) 10.42% D) 10.51% E) 10.6%
3. You want to accumulate at least 20000 in an account paying 4.5% annually by making a level deposit of 1000 at the beginning of the year for as long as necessary. Find the required number of deposits.
A) 13 B) 14 C) 15 D) 16 E) 11
4. Find the present value of the series of payments {500, 0, 200, 200, 300} with interest rate i = 5%.
A) 1105 B)1095 C)1100 D)1102 E) 1111
5. Kathryn deposits 100 into an account at the beginning of each 4-year period for 40 years. The account credits interest at an annual effective interest rate of i.
The accumulated amount in the account at the end of 40 years is X, which is 5 times the accumulated amount in the account at the end of 20 years. Calculate X.
A) 4695 B) 5070 C) 5445 D) 5820 E) 6195
6. Olga buys a 5-year increasing annuity for X. Olga will receive 2 at the end of the first month, 4 at the end of the second month and for each month thereafter the payment increases by 2. The nominal interest rate is 9% convertible quarterly. Calculate X.
A) 2680 B) 2730 C) 2780 D)2830 E)2880
7. Payments are made to an account at a continuous rate of (8k+tk), where 0 ≤ t ≤ 10. Interest is credited at a force of interest t = 1/(8+t). After 10 years, the account is worth 20,000. Calculate k.
A) 111 B) 116 C) 121 D) 126 E) 131
8. A perpetuity-immediate pays X per year. Brain receives the first n payments, Colleen receives the next n payments, and Jeff receives the remaining payments. Brian’s share of the present value of the original perpetuity is 40%, and Jeff’s share is K. Calculate K.
A) 24% B) 28% C) 32% D) 36% E) 40%
9. An insurance company has an obligation to pay the medical costs for a claimant. Average annual claims costs today are $5000, and medical inflation is expected to be 7% per year. The claimant is expected to live an additional 20 years. Claim payments are made at yearly intervals, with the first claim payment to be made one year from today.
Find the present value of the obligation if the annual interest rate is 5%.
A) 87932 B) 102514 C) 114611 D) 122634 E) Cannot be determined
10. At an annual effective interest rate of i, the present value of a perpetuity-immediate starting with a payment of 200 in the first year and increasing by 50 each year thereafter is 46,530. Calculate i.
A) 3.25% B) 3.50% C) 3.75% D) 4% E) 4.25%
11. Matthew makes a series of payments at the beginning of each year for 20 years. The first payment is 100. Each subsequent payment through the tenth year increases by 5% from the previous payment. After the tenth payment, each payment decreases 5% from the previous payment. Calculate the present value of these payments at the time the first payment is made using an annual effective rate of 7%.
A) 1375 B) 1385 C) 1395 D) 1405 E) 1415
12. Megan purchases a perpetuity-immediate for 3250 with annual payments of 130. At the same price and interest rate, Chris purchases an annuity-immediate with 20 annual payments that begin at amount P and increase by 15 each year thereafter. Calculate P.
A) 90 B) 116 C) 131 D) 176 E) 239
Model 2: Annuities and Perpetuities
1. A loan for 20000 must be repaid with 5 year end payments at an annual rate of 12%. What is the annual payment?
A) 5348 B) 5548 C) 5448 D) 5648 E) 5500
2. You have borrowed 15000 and agreed to repay the loan with 5 level payments of 4000, with the first payment occurring one year from today. What interest rate are you paying?
A) 10.1% B) 10.23% C) 10.42% D) 10.51% E) 10.6%
3. You want to accumulate at least 20000 in an account paying 4.5% annually by making a level deposit of 1000 at the beginning of the year for as long as necessary. Find the required number of deposits.
A) 13 B) 14 C) 15 D) 16 E) 11
4. Find the present value of the series of payments {500, 0, 200, 200, 300} with interest rate i = 5%.
A) 1105 B)1095 C)1100 D)1102 E) 1111
5. Kathryn deposits 100 into an account at the beginning of each 4-year period for 40 years. The account credits interest at an annual effective interest rate of i.
The accumulated amount in the account at the end of 40 years is X, which is 5 times the accumulated amount in the account at the end of 20 years. Calculate X.
A) 4695 B) 5070 C) 5445 D) 5820 E) 6195
6. Olga buys a 5-year increasing annuity for X. Olga will receive 2 at the end of the first month, 4 at the end of the second month and for each month thereafter the payment increases by 2. The nominal interest rate is 9% convertible quarterly. Calculate X.
A) 2680 B) 2730 C) 2780 D)2830 E)2880
7. Payments are made to an account at a continuous rate of (8k+tk), where 0 ≤ t ≤ 10. Interest is credited at a force of interest t = 1/(8+t). After 10 years, the account is worth 20,000. Calculate k.
A) 111 B) 116 C) 121 D) 126 E) 131
8. A perpetuity-immediate pays X per year. Brain receives the first n payments, Colleen receives the next n payments, and Jeff receives the remaining payments. Brian’s share of the present value of the original perpetuity is 40%, and Jeff’s share is K. Calculate K.
A) 24% B) 28% C) 32% D) 36% E) 40%
9. An insurance company has an obligation to pay the medical costs for a claimant. Average annual claims costs today are $5000, and medical inflation is expected to be 7% per year. The claimant is expected to live an additional 20 years. Claim payments are made at yearly intervals, with the first claim payment to be made one year from today.
Find the present value of the obligation if the annual interest rate is 5%.
A) 87932 B) 102514 C) 114611 D) 122634 E) Cannot be determined
10. At an annual effective interest rate of i, the present value of a perpetuity-immediate starting with a payment of 200 in the first year and increasing by 50 each year thereafter is 46,530. Calculate i.
A) 3.25% B) 3.50% C) 3.75% D) 4% E) 4.25%
11. Matthew makes a series of payments at the beginning of each year for 20 years. The first payment is 100. Each subsequent payment through the tenth year increases by 5% from the previous payment. After the tenth payment, each payment decreases 5% from the previous payment. Calculate the present value of these payments at the time the first payment is made using an annual effective rate of 7%.
A) 1375 B) 1385 C) 1395 D) 1405 E) 1415
12. Megan purchases a perpetuity-immediate for 3250 with annual payments of 130. At the same price and interest rate, Chris purchases an annuity-immediate with 20 annual payments that begin at amount P and increase by 15 each year thereafter. Calculate P.
A) 90 B) 116 C) 131 D) 176 E) 239