WEB APPENDIX 05A—CONTINUOUS COMPOUNDING AND DISCOUNTING
1. If you receive $15,000 today and can invest it at a 5% annual rate compounded continuously, what will be your ending
value after 20 years?
a.
$38,735.52
b.
$40,774.23
c.
$42,812.94
d.
$44,953.59
e.
$47,201.27
b
1
MODERATE
5A Continuous Compounding and Discounting
2. In six years’ time, you are scheduled to receive money from a trust established by your grandparents. When the trust
matures there will be $100,000 in the account. If the account earns 9% compounded continuously, how much is in the
account today?
a.
$55,361.08
b.
$58,274.83
c.
$61,188.57
d.
$64,247.99
e.
$67,460.39
b
1
MODERATE
5A Continuous Compounding and Discounting
3. Assume one bank offers you a nominal annual interest rate of 6% compounded daily while another bank offers you
continuous compounding at a 5.9% nominal annual rate. You decide to deposit $1,000 with each bank. Exactly two years
later you withdraw your funds from both banks. What is the difference in your withdrawal amounts between the two
banks?
a.
$2.24
b.
$2.35
c.
$2.47
d.
$2.59
e.
$2.72
a
N
1
MODERATE
5A Continuous Compounding and Discounting
4. You have $5,436.60 in an account that pays 10% interest, compounded continuously. If you deposited some funds 10
years ago, how much was your original deposit?
a.
$1,900
b.
$2,000
c.
$2,100
d.
$2,205
e.
$2,315
b
5. How much should you be willing to pay for an account today that will have a value of $1,000 in 10 years under
continuous compounding if the nominal rate is 10%?
a.
$349.49
b.
$367.88
c.
$386.27
d.
$405.59
e.
$425.87
b
1
MODERATE
5A Continuous Compounding and Discounting
6. You need a down payment of $19,000 in order to purchase your first home 4 years from today. You currently have
$14,014 to invest. In order to achieve your goal, what nominal interest rate, compounded continuously, must you earn on
this investment?
a.
7.61%
b.
7.99%
c.
8.39%
d.
8.81%
N
1
MODERATE
5A Continuous Compounding and Discounting
WEB APPENDIX 05A—CONTINUOUS COMPOUNDING AND DISCOUNTING
e.
9.25%
a
4i ln e
= ln 1.35579
4i
= 0.3044
= 7.61%
1
CHALLENGING
5A Continuous Compounding and Discounting
FOFM.BRIG.16.05.05A – Continuous Compounding and Discounting
United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills
United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money
Continuous compounded int. rate
Bloom’s: Application
Multiple Choice: Problem
7. You place $1,000 in an account that pays 7% interest compounded continuously. You plan to hold the account exactly 3
years. Simultaneously, in another account you deposit money that earns 8% compounded semiannually. If the accounts
are to have the same amount at the end of the 3 years, how much of an initial deposit do you need to make now in the
account that pays 8% interest compounded semiannually?
a.
$ 835.94
b.
$ 879.93
c.
$ 926.24
d.
$ 974.99
e.
$1,023.74
d
N
WEB APPENDIX 05A—CONTINUOUS COMPOUNDING AND DISCOUNTING
1
CHALLENGING
5A Continuous Compounding and Discounting
8. For a 10-year deposit, what annual rate payable semiannually will produce the same effective rate as 4% compounded
continuously?
a.
3.46%
b.
3.65%
c.
3.84%
d.
4.04%
e.
4.24%
d
N
1
CHALLENGING
5A Continuous Compounding and Discounting