Math

QuestionBen wants to buy a house for \$168,000. If it appreciates 1% annually, what will it be worth in 6 years? Round to the nearest dollar.

Studdy Solution

STEP 1

Assumptions1. The initial value of the house is $168,000. The annual increase in the value of the house is1%
3. The time period considered is6 years4. The increase in value is compounded annually5. The future value (V) factor is used to calculate the future value of the house

STEP 2

First, we need to calculate the future value (V) factor. The FV factor is calculated using the formulaVfactor=(1+Interestrate)NumberofyearsV\, factor = (1 + Interest\, rate)^{Number\, of\, years}

STEP 3

Now, plug in the given values for the interest rate and number of years to calculate the FV factor.
Vfactor=(1+1%)6V\, factor = (1 +1\%)^{6}

STEP 4

Convert the percentage to a decimal value.
1%=0.011\% =0.01Vfactor=(1+0.01)6V\, factor = (1 +0.01)^{6}

STEP 5

Calculate the FV factor.
Vfactor=(1+0.01)1.061V\, factor = (1 +0.01)^{} \approx1.061Remember to round the FV factor to3 decimal places.

STEP 6

Now that we have the FV factor, we can calculate the future value of the house. The future value is calculated by multiplying the initial value of the house by the FV factor.
Futurevalue=InitialvaluetimesFVfactorFuture\, value = Initial\, value \\times FV\, factor

STEP 7

Plug in the values for the initial value and the FV factor to calculate the future value.
Futurevalue=$168,000times1.061Future\, value = \$168,000 \\times1.061

STEP 8

Calculate the future value of the house.
Futurevalue=$168,000times1.061=$178,328Future\, value = \$168,000 \\times1.061 = \$178,328Remember to round the future value to the nearest whole dollar.
The approximate value of the house six years from now will be $178,328.

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