Chapter 5
Interest Rates
Note: All problems in this chapter are available in MyFinanceLab. An asterisk (*) indicates problems with a higher level of difficulty.
1. a. Becau six months is of two years, using our rule
So the equivalent six-month rate is 4.66%.
b. Becau one year is half of two years
So the equivalent one-year rate is 9.54%.我要买车
c. Becau one month is of two years, using our rule
So the equivalent one-month rate is 0.763%.
2. a. 0.06/12 = 0.005 or 0.5%
b. (1.005)12 – 1 = 0.0617 or 6.17%
3. Plan: The only way to compare the two rates is to convert them into their effective annual rates (EARs). To compute the EAR, you must first convert to the true rate at the appropriate compounding interval and then compound that rate over one year. The first rate is given as 15% compounded monthly, so you have to first compute the true monthly rate. The cond rate is already given as a six-month rate (8% every six months), so you just have to compound it to get the EAR:
Execute:
Evaluate:
You should u your credit card becau the effective annual rate is lower.
4. Plan: Becau the interest rates are quoted over different intervals, the only way to compare them is to compute the interest over a common interval. Here, the natural common interval to choo is three years.
Execute:
If you deposit $1 into a bank account that pays 5% per year for three years, you will have after three years.
a. If the account pays per six months, then you will have after
three years, so you prefer every six months.
b. If the account pays per 18 months, then you will have after
three years, so you prefer 5% per year.
c. If the account pays 1/2% per month then you will have after three years, so you prefer 1/2% every month.
Evaluate:
The comparisons are very difficult to make unless you put them on an equal footing (common interval). Once you do so, the better choice becomes clear.
*5. Plan: Draw a timeline to fully understand the timing of the cash flows. Determine the prent value of the bonus payments.
Execute:
0 | 7 | 14 | | | | 42 |
| | | | | | | | | | |
| | | | | 安卓怎么截图 | | | | | |
| | 50,000 | 50,000 | | | | 50,000 |
| | | | | | | |
| | | | | | | | | | |
Becau 鲈鱼养殖条件1.086 = 1.8509, the equivalent discount rate for a 6-year period is 85.09%.
Using the annuity formula
| N | I/Y | PV | PMT | FV | Excel Formula |
Given: | 8 | 85.09% | | 50,000 | 0 | |
Solve for PV: | | | (26817.76) | | | =PV(0.8509,8,50000,0) |
| | | | | | |
Evaluate: The PV of the annuity is $26,817.76.
6. Plan: Determine the EAR for each investment option.
Execute: For $1 invested in an account with 10% APR with monthly compounding you will have
So the EAR is 10.471%.
For $1 invested in an account with 10% APR with annual compounding, you will have
So the EAR is 10%.
For $1 invested in an account with 9% APR with daily compounding, you will have
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So the EAR is 9.416%.
Evaluate: One dollar invested at 10% APR compounded monthly will grow to $1.10471 in
one year. This is greater than the values for the other two investments and, therefore, is superior.
7. Plan: U the formula for converting from an EAR to an APR quote (Eq. 5.3).
Execute:
Solving for the APR
With annual payments k 形容人的句子= 1, so APR = 5%.
With miannual payments k = 2, so APR = 4.939%.
With monthly payments k = 12, so APR = 4.889%.
Evaluate:
The same effective annual rate can be quoted many different ways using different compounding periods.
8. Plan: Determine the prent value of the annuity.
Execute: Using the PV of an annuity formula with N = 30 payments and C = $500 with
r = 4.06% per 4-month interval becau there is a 12% APR with monthly compounding: 12%/12 = 1% per month, or (1.01)4 - 1 = 4.06% per four months.
| N | I/Y | PV | PMT | FV | Excel Formula |
Given: | 30 | 4.06% | | 冷嗖嗖500 | 0 | |
Solve for PV: | | | (8583.38) | | | =PV(0.0406,30,500,0) |
| | | | | | |
记忆中的美好时光Evaluate: The PV of the annuity is $8583.38.
9. The fee is just an interest payment. If you pay $30 for a $200 loan, that’s $30/$200 = 15% interest FOR TWO WEEKS! So your effective annual interest rate for this loan compounds the 15% over the 26 two-week periods in the year: (1.15)26 – 1 = 36.8568, or 3,685.68% !!
10. Plan: Draw a timeline to demonstrate when the tuition payments will be needed. Then calculate the PV of the tuition payments.
Execute:
0 | | 1 | | | | 4 |
0 | 1 | 2 | | | | 8 |
| | | | | | | | | | |
| | | | | | | | | | |
| | 10,000 | 10,000 | | | | 10,000 |
| | | | | | | | | | |
Four percent APR (miannual) implies a miannual discount rate of
So,
| N | I/Y | PV | PMT | FV新疆南疆旅游 | Excel Formula |
Given: | 8 | 2.000% | | 10000 | 0 | |
Solve for PV: | | | (73,254.81) | | | =PV(0.02,8,10000,0) |
| | | | | | |
Evaluate: You will have to deposit $73,254.81 in the bank today in order to be able to make the tuition payments over the next four years.
11. Plan: Compute the discount rate from the APR formula.
