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in 1990, the value of a home is $170,000. Since then, its value has increased 5% per year. what is the approximate value of a home in 1993?

Respuesta :

creamcheesebun

value of home in 1991= 105% of 170000

value of home in 1992= 105%×105% of 170000

value of home in 1993= 105%×105%×105% of 170000

=$196,796.25

The approximate value of the home in 1993 is $196,796.25

How to calculate compound interest's amount?

If the initial amount (also called as principal amount) is P, and the interest rate is R% per unit time, and it is left for T unit of time for that compound interest, then the interest amount earned is given by:

[tex]CI = P(1 +\dfrac{R}{100})^T - P[/tex]

The final amount becomes:

[tex]A = CI + P\\A = P(1 +\dfrac{R}{100})^T[/tex]

The increment in price would occur in similar manner as compound interest increases. It is because the 5% increment occurs on the last increased price.

For this case, we have:

  • Initial price of home in 1990: $170,000 = P
  • Rate of increment of price: 5% per year = R
  • Unit of time = year
  • Type of increment: Compound
  • Time for which increment happens = 1993 - 1990 = 3 years. = T

The final price of the home is then evaluated as:

[tex]A = P(1 + \dfrac{R}{100})^T = 170000(1+\dfrac{5}{100})^3 = 170000(1.05)^3\\\\A = 196796.25 \text{\: (in dollars)}[/tex]

Thus, the approximate value of the home in 1993 is $196,796.25

Learn more about compound interest here:

https://brainly.com/question/11897800

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