CHAPTER 6
B-77
Setting the two equal, we get:
(.07)(10) = (1 +
r
)
10
– 1
r
= 1.7
1/10
– 1 = .0545 or 5.45%
30.
Here we need to convert an EAR into interest rates for different compounding periods. Using the equation
for the EAR, we get:
EAR = [1 + (APR /
m
)]
m
– 1
EAR = .17 = (1 +
r
)
2
– 1;
r
= (1.17)
1/2
– 1
= .0817 or 8.17% per six months
EAR = .17 = (1 +
r
)
4
– 1;
r
= (1.17)
1/4
– 1
= .0400 or 4.00% per quarter
EAR = .17 = (1 +
r
)
12
– 1;
r
= (1.17)
1/12
– 1
= .0132 or 1.32% per month
Notice that the effective six month rate is not twice the effective quarterly rate because of the effect of
compounding.
31.
Here we need to find the FV of a lump sum, with a changing interest rate. We must do this problem in two
parts.
After the first six months, the balance will be:
FV = $5,000 [1 + (.015/12)]
6
= $5,037.62
This is the balance in six months. The FV in another six months will be:
FV = $5,037.62[1 + (.18/12)]
6
= $5,508.35
The problem asks for the interest accrued, so, to find the interest, we subtract the beginning balance
from the FV. The interest accrued is:
Interest = $5,508.35 – 5,000.00 = $508.35
32.
We need to find the annuity payment in retirement. Our retirement savings ends and the retirement
withdrawals begin, so the PV of the retirement withdrawals will be the FV of the retirement savings. So,
we find the FV of the stock account and the FV of the bond account and add the two FVs.
Stock account: FVA = $700[{[1 + (.11/12) ]
360
– 1} / (.11/12)] = $1,963,163.82
Bond account: FVA = $300[{[1 + (.06/12) ]
360
– 1} / (.06/12)] = $301,354.51
So, the total amount saved at retirement is:
$1,963,163.82 + 301,354.51 = $2,264,518.33