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QuestionCalculate the current value of a property bought for \$100,000, with house cost \$65,000, land appreciating at 5\% yearly.

Studdy Solution

STEP 1

Assumptions1. The original cost of the property is $100,000\$100,000 . The cost of building the house was $65,000\$65,000
3. The land has appreciated at 5%5\% per year for10 years4. The house has an economic life of40 years5. We are using the straight-line method for depreciation

STEP 2

First, we need to find the original cost of the land. We can do this by subtracting the cost of the house from the total cost of the property.
Cost of land=Total cost−Cost of houseCost\, of\, land = Total\, cost - Cost\, of\, house

STEP 3

Now, plug in the given values for the total cost and the cost of the house to calculate the cost of the land.
Cost of land=$100,000−$65,000Cost\, of\, land = \$100,000 - \$65,000

STEP 4

Calculate the cost of the land.
Cost of land=$100,000−$65,000=$35,000Cost\, of\, land = \$100,000 - \$65,000 = \$35,000

STEP 5

Next, we need to calculate the appreciated value of the land. We can do this by multiplying the original cost of the land by 11 plus the appreciation rate, raised to the power of the number of years.
Appreciated value of land=Cost of landtimes(1+Appreciation rate)YearsAppreciated\, value\, of\, land = Cost\, of\, land \\times (1 + Appreciation\, rate)^{Years}

STEP 6

Convert the appreciation rate to a decimal value.
5%=0.055\% =0.05

STEP 7

Now, plug in the given values for the cost of the land, the appreciation rate, and the number of years to calculate the appreciated value of the land.
Appreciated value of land=$35,000times(1+0.05)10Appreciated\, value\, of\, land = \$35,000 \\times (1 +0.05)^{10}

STEP 8

Calculate the appreciated value of the land.
Appreciated value of land=$35,000times(1+0.05)10=$57,155.13Appreciated\, value\, of\, land = \$35,000 \\times (1 +0.05)^{10} = \$57,155.13

STEP 9

Next, we need to calculate the depreciated value of the house using the straight-line method. This is done by dividing the cost of the house by its economic life, and then multiplying by the number of years passed.
Depreciated value of house=Cost of house−(Cost of house/Economic lifetimesYears)Depreciated\, value\, of\, house = Cost\, of\, house - (Cost\, of\, house / Economic\, life \\times Years)

STEP 10

Now, plug in the given values for the cost of the house, the economic life, and the number of years to calculate the depreciated value of the house.
Depreciated value of house=$65,000−($65,000/40times10)Depreciated\, value\, of\, house = \$65,000 - (\$65,000 /40 \\times10)

STEP 11

Calculate the depreciated value of the house.
Depreciated value of house=$65,000−($65,000/40times10)=$48,750Depreciated\, value\, of\, house = \$65,000 - (\$65,000 /40 \\times10) = \$48,750

STEP 12

Finally, we can calculate the current value of the property by adding the appreciated value of the land to the depreciated value of the house.
Current value of property=Appreciated value of land+Depreciated value of houseCurrent\, value\, of\, property = Appreciated\, value\, of\, land + Depreciated\, value\, of\, house

STEP 13

Now, plug in the calculated values for the appreciated value of the land and the depreciated value of the house to calculate the current value of the property.
Current value of property=$57,155.13+$48,750Current\, value\, of\, property = \$57,155.13 + \$48,750

STEP 14

Calculate the current value of the property.
Current value of property=$57,155.13+$48,750=$105,905.13Current\, value\, of\, property = \$57,155.13 + \$48,750 = \$105,905.13The property's current value is $105,905.13\$105,905.13.

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