Appendix 5A Continuous Compounding and Discounting
Answers and Solutions
5A–1
Web Appendix 5A
Continuous Compounding and Discounting
Solutions to Problems
5A-1 FV15 = $15,000e0.06(15) = $36,894.05.
5A-3 Daily compounding:
FV2 = PV(1 + 0.07/365)365(2) = $1,000(1.15026) = $1,150.26
5A-4 Calculate the growth factor using PV and FV which are given:
FVN = PVeIN; $40,000 = $20,000eI6
eI6 = 2.0.
Take the natural logarithm of both sides:
I(6)ln e = ln 2.00.
5A-5 Determine the effective annual rates.
10.25% annually = 10.25%.
10.1% semiannually =
2
2
101.0
1
+
– 1.0 = 0.1036 = 10.36%.
5A–2
Answers and Solutions
Appendix 5A Continuous Compounding and Discounting
5A-6 (Constant e = 2.7183 rounded.)
$11,572.28 = PVe0.09(15)
5A-7 e(0.03)(10) =
20
NOM
2
I
1
+
e0.3 =
20
NOM
2
I
1
+
5A-8 Step 1: Calculate the FV of the $2,000 deposit at 8% with continuous compounding:
Using ex key: