Interest Compounding, Frequency, Future Value and Present Value

1. Compounding frequency and future value

You plan to invest $2,000 in an individual retirement account (IRA) today at a nominal rate of 8 percent, which is expected to apply to all future years.

a. How much will you have in the account after 10 years if the interest is compounded:
1. Annually
2. Semi-Annually
3. Daily (assume a 360-day year)
4. Continuously

b. What is the effective annual rate, EAR, for each compounding period in a?

c. How much greater will your account balance be at the end of ten years if interest is compounded continuously rather than annually?

d. How does the compounding frequency affect the future value and effective annual rate for a given deposit? Explain in terms of your finding in a through c.

You just won a lottery that promises to pay you $1,000,000 exactly 10 years from today. Because the $1,000,000 payment is guaranteed by the state in which you live, opportunities exist to sell the claim today for an immediate lump sum cash payment.

a. What is the least you would sell your claim for if you could earn the following rates of return on similar-risk investments during the 10-year period?
1. 6 percent
2. 9 percent
3. 12 percent

b. Rework (a) under the assumption that the $1,000,000 payment will be received in 15 rather than 10 years.

c. Based on your findings in (a) and (b), discuss the effect of both the size of the rate of return and the time until receipt of payment on the present value of a future sum.

3. Funding your retirement

You plan to retire in exactly 20 years. Your goal is to create a fund that will allow you to receive $20,000 per year for 30 years between retirement and death (a physic told you would die after 30 years). You know that you will be able to earn 11 percent per year during the 30-year retirement period.

a. How large a fund will you need when you retire in 20 years to provide the 30-year, $20,000 retirement annuity?

b. How much would you need today as a lump sum to provide the amount calculated in (a) if you earn only 9 percent per year during the 20 years preceding retirement?

c. What effect would an increase in the rate could earn both during and prior to retirement have on the values found in (a) and (b)?

Show the formula used in the following questions in detail
1)
a. What is the futurevalue of $4,000 invested at 6% for 22 years with annual compounding?
b. What is the futurevalue of $4,000 invested at 6% for 22 years with monthly compounding?
c. What is the futurevalue of $4,000 invested at 6% for 22 years with cont

A. Table Factor X, FutureValue $X
PresentValue Rate Time Compounding Frequency Table Factor FutureValue
a. $5,000 12% 2 yrs Annual
b. $5,000 12% 2 yrs Semiannual
c. $5,000 12% 2 yrs. Quarterly
d. $5,000 12%

? Calculate the futurevalue of the following:
?
o $5,000 compounded annually at 6% for 5 years
o $5,000 compounded semiannually at 6% for 5 years
o $5,000 compounded quarterly at 6% for 5 years
o $5,000 compounded annually at 6% for 6 years
?
? Answer the following: What conclusions can be drawn about the frequen

25. The stated rate of interest is 10%. Which form of compounding will give the highest effective rate of interest?
A. annual compounding
B. monthly compounding
C. daily compounding
D. continuous compounding
E. It is impossible to tell without knowing the term of the loan.

P3-21. You plan to invest $2,000 in an individual retirement arrangement (IRA) today at a stated interest rate of 8 percent, which is expected to apply to all future years.
a. How much will you have in the account at the end of 10 years if interest is compounded as follows?
(1) Annually
(2) Semiannually
(3) Daily (assume

How would you calculate the presentandfuturevalue of the following annuity streams?
a. $5,000 received each year for 5 years on the last day of each year if your investments pay 6 percent compounded annually.
b. $5,000 received each quarter for 5 years on the last day of each quarter if your investments pay 6 percent co

WHAT IS THE VALUE AT THE END OF YEAR 3 OF THE FOLLOWING CASH FLOW STREAM IF THE QUOTED INTEREST RATE IS 10 PERCENT, COMPOUNDED SEMIANNUALLY?
0 2 4 6 PERIODS
| | | |
100 100 100

Problem 1
If interest rates are 8 percent, what is the futurevalue of a $400 annuity payment over six years? Unless otherwise directed, assume annual compounding periods.
- Recalculate the futurevalue at 6 percent interestand 9 percent interest.
Problem 2
If interest rates are 5 percent, what is the presentvalue of a

13. The futurevalue of $200 received today and deposited for three years in an account which pays semiannual interest of 8 percent is ______.
A. $253.00
B. $252.00
C. $158.00
D. $134.66
14. The futurevalue of $100 received today and deposited at 6 percent for four years is
A. $126.
B. $ 79.
C. $124.
D. $116.
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