CHAPTER 6
B-89
60.
To find the APR and EAR, we need to use the actual cash flows of the loan. In other words, the interest rate
quoted in the problem is only relevant to determine the total interest under the terms given. The cash flows
of the loan are the $25,000 you must repay in one year, and the $21,250 you borrow today. The interest rate
of the loan is:
$25,000 = $21,250(1 +
r
)
r
= ($25,000 / 21,250) – 1 = .1765 or 17.65%
Because of the discount, you only get the use of $21,250, and the interest you pay on that amount is
17.65%, not 15%.
61.
Here we have cash flows that would have occurred in the past and cash flows that would occur in the
future. We need to bring both cash flows to today. Before we calculate the value of the cash flows today,
we must adjust the interest rate so we have the effective monthly interest rate. Finding the APR with
monthly compounding and dividing by 12 will give us the effective monthly rate. The APR with monthly
compounding is:
APR = 12[(1.08)
1/12
– 1] = .0772 or 7.72%
To find the value today of the back pay from two years ago, we will find the FV of the annuity, and then
find the FV of the lump sum. Doing so gives us:
FVA = ($47,000/12) [{[ 1 + (.0772/12)]
12
– 1} / (.0772/12)] = $48,699.39
FV = $48,699.39(1.08) = $52,595.34
Notice we found the FV of the annuity with the effective monthly rate, and then found the FV of the lump
sum with the EAR. Alternatively, we could have found the FV of the lump sum with the effective monthly
rate as long as we used 12 periods. The answer would be the same either way.
Now, we need to find the value today of last year’s back pay:
FVA = ($50,000/12) [{[ 1 + (.0772/12)]
12
– 1} / (.0772/12)] = $51,807.86
Next, we find the value today of the five year’s future salary:
PVA = ($55,000/12){[{1 – {1 / [1 + (.0772/12)]
12(5)
}] / (.0772/12)}= $227,539.14