CHAPTER 6
B-73
14.
For discrete compounding, to find the EAR, we use the equation:
EAR = [1 + (APR /
m
)]
m
– 1
So, for each bank, the EAR is:
First National:
EAR = [1 + (.1420 / 12)]
12
– 1 = .1516 or 15.16%
First United:
EAR = [1 + (.1450 / 2)]
2
– 1 = .1503 or 15.03%
Notice that the higher APR does not necessarily mean the higher EAR. The number of compounding
periods within a year will also affect the EAR.
15.
The reported rate is the APR, so we need to convert the EAR to an APR as follows:
EAR = [1 + (APR /
m
)]
m
– 1
APR =
m
[(1 + EAR)
1/
m
– 1]
APR = 365[(1.16)
1/365
– 1] = .1485 or 14.85%
This is deceptive because the borrower is actually paying annualized interest of 16% per year, not the
14.85% reported on the loan contract.
16.
For this problem, we simply need to find the FV of a lump sum using the equation:
FV = PV(1 +
r)
t
It is important to note that compounding occurs semiannually. To account for this, we will divide the
interest rate by two (the number of compounding periods in a year), and multiply the number of periods by
two. Doing so, we get:
FV = $2,100[1 + (.084/2)]
34
= $8,505.93
17.
For this problem, we simply need to find the FV of a lump sum using the equation:
FV = PV(1 +
r)
t
It is important to note that compounding occurs daily. To account for this, we will divide the interest rate
by 365 (the number of days in a year, ignoring leap year), and multiply the number of periods by 365.
Doing so, we get:
FV in 5 years
= $4,500[1 + (.093/365)]
5(365)
= $7,163.64
FV in 10 years = $4,500[1 + (.093/365)]
10(365)
= $11,403.94
FV in 20 years = $4,500[1 + (.093/365)]
20(365)
= $28,899.97