Finite maths
1. Use the “rule of 72” to estimate the doubling time (in years) for the interest rate, and then calculate it exactly (Round your answers to two decimal places.)
8% compounded annually
“rule of 72” _________years
exact answer _________years
2. Use the “rule of 72” to estimate the doubling time (in years) for the interest rate, and then calculate it exactly. (Round your answers to two decimal places.)
7.4% compounded weekly
“rule of 72” _________years
exact answer _________years
3. Find the effective rate of the compound interest rate or investment. (Round your answers to two decimal places.)
28% compounded monthly [Note: This rate is a typical credit card interest rate, often stated as 2.3% per month]
_________%
4. Find the effective rate of the compound interest rate or investment. (Round your answers to two decimal places.)
A $70,000 zero-coupon bond maturing in 8 years and selling now for $46,035
_________%
5. You have just received $165,000 from the estate of a long-lost rich uncle. If you invest all your inheritance in a tax-free bond fund earning 6.1% compounded quarterly, how long do you have to wait to become a millionaire? (Round your answer to two decimal places.)
_________years
6. The Second Peoples National Bank offers a long-term certificate of deposit earning 6.53% compounded monthly. Your broker locates $20,000 zero-coupon bond rated AA by Standard & Poor’s $8965 and maturing in 14 years. Which investment will give the greater of return?
a. The Second Peoples National Bank offers a better rate of return
b. The zero-coupon bond offers a better rate of return
7. You have just won $130,000 from a lottery. If you invest all this amount in a tax-free money market fund earning 8% compounded weekly, how long do you have to wait to become a millionaire? (Round your answer to two decimal places.)
_________years
8. In the following ordinary annuity, the interest is compounded with each payment, and the payment is made at the end of the compounding period.
Find the accumulated amount of the annuity. (Round your answer to the nearest cent.)
$3500 annually at 6% for 10 years.
$_________
9. In the following ordinary annuity, the interest is compounded with each payment, and the payment is made at the end of the compounding period.
Find the accumulated amount of the annuity. (Round your answer to the nearest cent.)
$_________
10. In the following ordinary annuity, the interest is compounded with each payment, and the payment is made at the end of the compounding period. Find the required payment for the sinking fund. (Round your answer to the nearest cent.)
Monthly deposits earning 4% to accumulate $7000 after 10 years
$_________
11. In the following ordinary annuity, the interest is compounded with each payment, and the payment is made at the end of the compounding period. Find the required payment for the sinking fund. (Round your answer to the nearest cent.)
Yearly deposits earning 12.8% to accumulate $6500 after 12 years.
$_________
12. In the following ordinary annuity, the interest is compounded with each payment, and the payment is made at the end of the compounding period. Find the amount of time needed for the sinking fund to reach the given accumulated amount. (Round your answer to two decimal places.)
$275 monthly at 5.5% to accumulate $25,000.
_________years
13. In the following ordinary annuity, the interest is compounded with each payment, and the payment is made at the end of the compounding period. An individual retirement account, or IRA, earns tax-deferred interest and allows the owner to invest up to $5000 each year. Joe and Jill both will make IRA deposits for 30 years (from age 35 to 65) into stock mutual funds yielding 9.7%. Joe deposits $5000 once each year, while Jill has $96.15 (which is 5000/52) withheld from her weekly paycheck and deposited automatically. How much will each have at age 65? (Round your answer to the nearest cent.)
Joe $_________
Jill $_________
14. In the following ordinary annuity, the interest is compounded with each payment, and the payment is made at the end of the compounding period. How much must you invest each month in a mutual fund yielding 11.8% compounded monthly to become a millionaire in 10 years? (Round your answer to the nearest cent.)
$_________
15. In the following ordinary annuity, the interest is compounded with each payment, and the payment is made at the end of the compounding period. The Oseola McCarty Scholarship Fund at the University of Southern Mississippi was established by a $170,000 gift from an 87-year-old woman who had dropped out of sixth grade and worked for most of her life as a washerwoman. How much would she have had to save each week in a bank account earning 3.9% compounded weekly to have $170,000 after 75 years? (Round your answer to the nearest cent.)
$_________
16. In the following ordinary annuity, the interest is compounded with each payment, and the payment is made at the end of the compounding period. You and your new spouse each bring home $1600 each month after taxes and other payroll deductions. By living frugally, you intend to live on just one paycheck and save the other in a mutual fund yielding 7.96% compounded monthly. How long will it take to have enough for a 20% down payment on a $175,000 condo in the city? (Round your answer to two decimal places.)
_________years
17. Calculate the present value of the annuity. (Round your answer to the nearest cent.)
$1600 monthly at 6.2% for 30 years.
$_________
18. Determine the payment to amortize the debt. (Round your answer to the nearest cent.)
Monthly payments on $160,000 at 3% for 25 years.
$_________
19. Determine the payment to amortize the debt. (Round your answer to the nearest cent.)
Quarterly payments on $14,500 at 3.5% for 6 years.
$_________
20. Find the unpaid balance on the debt. (Round your answer to the nearest cent.)
After 6 years of monthly payments on $170,000 at 3% for 25 years.
$_________
21. The super prize in a contest is $10 million. This prize will be paid out in equal yearly payments over the next 25 years. If the prize money is guaranteed by AAA bonds yielding 4% and is placed into an escrow account when the contest is announced 1 year before the first payment, how much do the contest sponsors have to deposit in the escrow account? (Round your answer to the nearest cent.)
$_________
22. Just before his first attempt at bungee jumping, John decides to buy a life insurance policy. His annual income at age 30 is $39,000, so he figures he should get enough insurance to provide his wife and new baby with that amount each year for the next 35 years. If the long-term interest rate is 6.3%, what is the present value of John’s future annual earnings? (Round your answer to the nearest cent.)
$_________
23. A MasterCard statement shows a balance of $560 at 13.4% compounded monthly. What monthly payment will pay off this debt in 1 year 8 months? (Round your answer to the nearest cent.)
$_________
24. Find the simple interest on the loan.
$1200 at 7% for 10 years.
$_________
25. Find the total amount due for the simple interest loan.
$1100 at 8% for 10 years.
$_________
·
· 26. Find the interest rate on a loan charging $1083 simple interest on a principal of $4750 after 6 years.
_________%
·
· 27. Find the term of a loan of $400 at 3.5% if the simple interest is $28.
_________years
28. Determine the amount due on the compound interest loan. (Round your answers to the nearest cent.)
$18,000 at 3% for 10 years if the interest is compounded in the following ways.
(a) annually $_________
(b) quarterly $_________
29. Calculate the present value of the compound interest loan. (Round your answers to the nearest cent.)
$24,000 after 7 years at 4% if the interest is compounded in the following ways.
(a) annually $_________
(b) quarterly $_________
·
· 30. Find the term of the compound interest loan. (Round your answer to two decimal places.)
5.9% compounded quarterly to obtain $8100 from a principal of $2000.
_________years
31. Use the “rule of 72” to estimate the doubling time (in years) for the interest rate, and then calculate it exactly. (Round your answers to two decimal places.)
8% compounded annually.
“rule of 72” _________years
exact answer _________years
32. Find the effective rate of the compound interest rate or investment. (Round your answer to two decimal places.)
28% compounded monthly. [Note: This rate is a typical credit card interest rate, often stated as 2.3% per month.]
_________%
·
· 33. Since 2007, a particular fund returned 13.5% compounded monthly. How much would a $5000 investment in this fund have been worth after 3 years? (Round your answer to the nearest cent.)
$_________
·
· 34. In the following ordinary annuity, the interest is compounded with each payment, and the payment is made at the end of the compounding period.
Find the accumulated amount of the annuity. (Round your answer to the nearest cent.)
$3500 annually at 5% for 10 years.
$_________
·
35. In the following ordinary annuity, the interest is compounded with each payment, and the payment is made at the end of the compounding period. Find the required payment for the sinking fund. (Round your answer to the nearest cent.)
Monthly deposits earning 6% to accumulate $7000 after 10 years.
$_________
·
· 36. In the following ordinary annuity, the interest is compounded with each payment, and the payment is made at the end of the compounding period. Find the amount of time needed for the sinking fund to reach the given accumulated amount. (Round your answer to two decimal places.)
$2500 yearly at 8% to accumulate $100,000.
_________years
·
· 37. In the following ordinary annuity, the interest is compounded with each payment, and the payment is made at the end of the compounding period.
An individual retirement account, or IRA, earns tax-deferred interest and allows the owner to invest up to $5000 each year. Joe and Jill both will make IRA deposits for 30 years (from age 35 to 65) into stock mutual funds yielding 9.7%. Joe deposits $5000 once each year, while Jill has $96.15 (which is 5000/52) withheld from her weekly paycheck and deposited automatically. How much will each have at age 65? (Round your answer to the nearest cent.)
Joe $_________
Jill $_________
·
38. In the following ordinary annuity, the interest is compounded with each payment, and the payment is made at the end of the compounding period.
How much must you invest each month in a mutual fund yielding 11.7% compounded monthly to become a millionaire in 10 years? (Round your answer to the nearest cent.)
$_________
·
· 39. Calculate the present value of the annuity. (Round your answer to the nearest cent.)
$17,000 annually at 6% for 10 years.
$_________
·
40. Determine the payment to amortize the debt. (Round your answer to the nearest cent.)
Monthly payments on $160,000 at 3% for 25 years.
$_________
·
·
· 41. Determine the payment to amortize the debt. (Round your answer to the nearest cent.)
Quarterly payments on $14,500 at 3.5% for 6 years.
$_________
·
· 42. Find the unpaid balance on the debt. (Round your answer to the nearest cent.)
After 5 years of monthly payments on $170,000 at 3% for 25 years.
$_________
·
43. The super prize in a contest is $10 million. This prize will be paid out in equal yearly payments over the next 25 years. If the prize money is guaranteed by AAA bonds yielding 4% and is placed into an escrow account when the contest is announced 1 year before the first payment, how much do the contest sponsors have to deposit in the escrow account? (Round your answer to the nearest cent.)
$_________
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