18.9: Finance
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1. A=200+.05(200)=$210
3. I=200.t=13/52(13 weeks out of 52 in a year ).P0=9800
200=9800(r)(13/52)r=0.0816=8.16% annual rate
5. P10=300(1+.05/1)10(1)=$488.67
7.
- P20=2000(1+.03/12)20(12)=$3641.51 in 20 years
- 3641.51−2000=$1641.51 in interest
9. P8=P0(1+.06/12)8(12)=6000⋅P0=$3717.14 would be needed
11.
- P30=200((1+0.03/12)30(12)−1)0.03/12=$116,547.38
- 200(12)(30)=$72,000
- $116,547.40−$72,000=$44,547.38 of interest
13.
- P30=800,000=d((1+0.06/12)30(12)−1)0.06/12d=$796.40 each month
- $796.40(12)(30)=$286,704
- $800,000−$286,704=$513,296 in interest
15.
- P0=30000(1−(1+0.08/1)−25(1))0.08/1=$320,243.29
- 30000(25)=$750,000
- $750,000−$320,243.29=$429,756.71
17. P0=500,000=d(1−(1+0.06/12)−20(12))0.06/12d=$3582.16 each month
19.
P0=700(1−(1+0.05/12)−30(12))0.05/12= a $130,397.13 loan
700(12)(30)=$252,000
$252,200−$130,397.13=$121,602.87 in interest
21. P0=25,000=d(1−(1+0.02/12)−48)0.02/12=$542.38 a month
23.
Down payment of 10% is $20,000, leaving $180,000 as the loan amount
P0=180,000=d(1−(1+0.05/12)−30(12))0.05/12d=$966.28amonth
P0=180,000=d(1−(1+0.06/12)−30(12))0.06/12d=$1079.19 a month
25. First we find the monthly payments:
P0=24,000=d(1−(1+0.03/12)−5(12))0.03/12⋅d=$431.25
Remaining balance: P0=431.25(1−(1+0.03/12)−2(12))0.03/12=$10,033.45
27. 6000(1+0.04/12)12N=10000
(1.00333)12N=1.667
log((1.00333)12N)=log(1.667)
12Nlog(1.00333)=log(1.667)
N=log(1.667)12log(1.00333)= about 12.8 years
29. 3000=60(1−(1+0.14/12)−12N)0.14/12
3000(0.14/12)=60(1−(1.0117)−12N)
3000(0.14/12)60=0.5833=1−(1.0117)−12N
0.5833−1=−(1.0117)−12N
−(0.5833−1)=(1.0117)−12N
log(0.4167)=log((1.0117)−12N)
log(0.4167)=−12Nlog(1.0117)
N=log(0.4167)−12log(1.0117)= about 6.3 years
31. First 5 years: P5=50((1+0.08/12)5(12)−1)0.08/12=$3673.84
Next 25 years: 3673.84(1+.08/12)25(12)=$26,966.65
33. Working backwards, P0=10000(1−(1+0.08/4)−10(4))0.08/4=$273,554.79 needed at retirement. To end up with that amount of money, 273,554.70=d((1+0.08/4)15(4)−1)0.08/4. He’ll need to contribute d=$2398.52 a quarter.