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Kari would like to save $10,000 for a down payment on a house. Illustrate the difference in years it will take her to double her current $5,000 savings based on a 6%, 12%, and 18% interest rate.

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Edufirst

Answer:

  • For 6%, approximately 12 years
  • For 12%, approximately 6 years
  • For 18%, approximately 4 years

Explanation:

The growing of the $10,000 will depend on the number of times the interest is compounded per year.

For didactic purposes, the period of compounding will be annual (once per year)

Formula:

      [tex]Future\text{ }Value=Investment\times (1+r/n)^{(n\times t)}[/tex]

  • n is the number of times the interest is compounde per year: 1
  • t is the numbrer of years
  • r is the annual percantage rate (APR)

Then:

    [tex]\$10,000=\$5,000\times (1+r)^{ t}[/tex]

         [tex](1+r)^{ t}=\$10,000/\$5,000\\\\(1+r)^t=2\\\\t\times \log (1+r)=\log 2\\\\\\t=\log 2/\log {(1+r)}[/tex]

For r = 6 %, r = 0.06

      [tex]t=\log 2/\log {(1+0.06)}=11.9\approx 12years[/tex]

For r = 12%

      [tex]t=\log 2/\log {(1+0.12)}=6.1\approx 6years[/tex]

For r = 18%

      [tex]t=\log 2/\log {(1+0.18)}=4.2\approx 4years[/tex]

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