Solutions to Chapter 3 Knowledge Checks
Knowledge Check 3.1
- P = $3,000; r = 6% = 0.06; t =180/365 years
- I=$55; r =5.5%=0.055; t =125/365 years
- P = $900, I = $65, r = 7.5% = 0.075
To convert this answer to days, you must multiply by 365. To eliminate a rounding error, be sure to use the exact value from your calculator, i.e., just multiply the above value by 365 without re-entering the displayed value .
This should now be rounded up to 352 days.
- P = $975, I = $36.73, t =220/365 years
Knowledge Check 3.2
- P = $4,000, r = 8% = 0.08, t = 210/365 years
- P = $1,250, r = 6.75% = 0.0675;
years (from Table 3- 1)
- P = $2,500, r = 3.75% = 0.0375, t = 2 years
Knowledge Check 3.3
- P = $2,000, FV = $2,210, t = 1.5 years
Either of the two following approaches is acceptable:
Approach A:
So
Approach B:
- FV = $1,871.25, r = 9% = 0.09, t = 33 months =33/12 years.
Knowledge Check 3.4
a. Find FV at 7%:
Conclusion: The value of $10,000 now, in six months’ time is $10,350. Since this is $25 greater than $10,325, you would prefer $10,000 now from a purely financial point of view.
b. Find FV at 6%:
Conclusion: The value of $10,000 now, in six months time is $10,300. Since this is less than $10,325, you would prefer $10,325 in six months time.
Knowledge Check 3.5
Total Debt Outstanding = $37,733.33(6 months from now)
Knowledge Check 3.6
1.
Total Equivalent Debt Now = $5,639.59
Knowledge Check 3.8
Value of “old” payments at the focal date :
Value of “replacement” payments at the focal date:
Therefore:
Knowledge Check 3.9
Let the amount of two equal payments be x. Value of “old” payments at the focal date:
Value of “replacement” payments at the focal date:
And we can set these to be equal:
And solve, remembering to store all intermediate values in the calculator:
Therefore: The size of the two equal payments is $9,794.38.