MATH 253 THEORY OF INTEREST
CHAPTER 3 - EXTRA QUESTIONS
1. Find the present value at t=0 of payments of $100 per year payable at the end of the year for the next 15 years.
2. Find the accumulated value of the payments above, on the date of the last payment.
3. Find the accumulated value of the payments in question 1 above, 1 year after the last payment.
4. Find the current value at time t=5 of the payments in question 1 above.
5. Find the present value at t=0 of 15 payments of $100 per year payable at the beginning of the year.
6. Glenn wants to accumulate $10,000 in a fund at the end of ten years. If , and he makes payments at the end of every month, what is the amount of the monthly payment?
7. Find the amount of the payment in question 6 above if , and Glenn makes the payments at the end of every quarter.
8. If the present value of an annuity of X per year, payable at the end of each year for 20 years is $5,000, what is the accumulated value at the end of 20 years?
9. Laurel purchases an annuity for $7500. Starting in three months, she will withdraw an amount $X every quarter for 4 years. At that time, the fund will be = $0. Calculate X.
10. Kim gets a loan of $25,000 that is to be paid back with quarterly payments with first payment in three months, for 15 years. If ,what is the amount of each loan payment?
11.A perpetuity due is purchased for $120,000. If interest is 8% effective, what is the amount of the annual payment?
12. What is the total amount of interest paid on a loan of $15,000, if interest is 5% convertible semiannually and payments are made every 6 months (starting 6 months after the loan) for 7 years?
13. Show that
14. Show that
15. What is the accumulated value at the end of 7 years, of payments of $100 at the end of every month for 3 years, and $250 at the end of every month for the following 4 years?
16. What is the present value at t=0 of the payments in question 15 above?
17. What is the present value at t=0 of the payments in question 15 above, if payments are made at the beginning of the month?
18. What is the accumulated value of payments of $1000 every 6 months for 10 years, 5 years after the last payment date?
19. What is the present value of payments of $250 every quarter payable for 3 years at , 9 months before the first payment date?
20. Joe leaves an estate of $100,000 to his wife and to a certain charity. His wife is to receive payments of $10,000 at the end of every year for 10 years. The remaining money will be used to purchase a perpetuity beginning at the end of the 11th year for the charity. What annual payment will the charity receive?
21. Jim gets a loan of $10000 which he plans to pay back with payments of $150 per month, first payment starting in one month. How long must he make payments? What is the size of the final payment if it is made one month after the last full payment?
Answers
1. $971.22
2. $2327.60
3. $2467.26
4. $1299.72
5. $1029.50
6. $61.02 per month
7. $184.27 per quarter
- $13266.49 or $13266.39 depending on how you do the question.
- $552.38
- $719.20
- $8888.89 per year
- $1283.05
- $20270.80
- $10821.47
- $10902.64
- $39821.28
- $2541.17 or $2541.10
- $1855.53
- $114.97