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Mathematics LibreTexts

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.

  1. P20=2000(1+.03/12)20(12)=$3641.51 in 20 years
  2. 3641.512000=$1641.51 in interest

9. P8=P0(1+.06/12)8(12)=6000P0=$3717.14 would be needed

11.

  1. P30=200((1+0.03/12)30(12)1)0.03/12=$116,547.38
  2. 200(12)(30)=$72,000
  3. $116,547.40$72,000=$44,547.38 of interest

13.

  1. P30=800,000=d((1+0.06/12)30(12)1)0.06/12d=$796.40 each month
  2. $796.40(12)(30)=$286,704
  3. $800,000$286,704=$513,296 in interest

15.

  1. P0=30000(1(1+0.08/1)25(1))0.08/1=$320,243.29
  2. 30000(25)=$750,000
  3. $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))0.03/12d=$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

0.58331=(1.0117)12N

(0.58331)=(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.


This page titled 18.9: Finance is shared under a CC BY-SA 3.0 license and was authored, remixed, and/or curated by David Lippman (The OpenTextBookStore) via source content that was edited to the style and standards of the LibreTexts platform.

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