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QuestionFind the 2014 annual rates for a flat with a 2.5% yearly increase, starting from \$5200 per quarter in 2008.

Studdy Solution

STEP 1

Assumptions1. The rateable value of the flat increases at a constant rate of.5% per year. . The owner paid rates of $5200 per quarter in2008.
3. We need to find the annual rates that the owner should pay in2014.
4. The rates increase annually, not quarterly.

STEP 2

First, we need to find the annual rates in2008. Since the owner paid $5200 per quarter, we can multiply this by4 (the number of quarters in a year) to find the annual rates.
Annual rates (2008)=Quarterly ratestimesNumber of quartersAnnual\, rates\, (2008) = Quarterly\, rates \\times Number\, of\, quarters

STEP 3

Now, plug in the given values for the quarterly rates and the number of quarters to calculate the annual rates in2008.
Annual rates (2008)=$5200timesAnnual\, rates\, (2008) = \$5200 \\times

STEP 4

Calculate the annual rates in2008.
Annual rates (2008)=$5200times4=$20800Annual\, rates\, (2008) = \$5200 \\times4 = \$20800

STEP 5

Now that we have the annual rates in2008, we can calculate the annual rates in2014. Since the rateable value increases at a constant rate of2.5% per year, we can multiply the annual rates in2008 by (1+2.5%)n(1 +2.5\%)^{n}, where nn is the number of years between2008 and2014.
Annual rates (2014)=Annual rates (2008)times(1+2.5%)nAnnual\, rates\, (2014) = Annual\, rates\, (2008) \\times (1 +2.5\%)^{n}

STEP 6

Convert the percentage to a decimal value.
2.5%=0.0252.5\% =0.025Annual rates (2014)=Annual rates (2008)times(1+0.025)nAnnual\, rates\, (2014) = Annual\, rates\, (2008) \\times (1 +0.025)^{n}

STEP 7

Calculate the number of years between200 and2014.
n=2014−200=6n =2014 -200 =6Annual rates (2014)=Annual rates (200)times(1+0.025)6Annual\, rates\, (2014) = Annual\, rates\, (200) \\times (1 +0.025)^{6}

STEP 8

Now, plug in the values for the annual rates in2008, the decimal value of the percentage increase, and the number of years to calculate the annual rates in2014.
Annual rates (2014)=$20800times(1+0.025)6Annual\, rates\, (2014) = \$20800 \\times (1 +0.025)^{6}

STEP 9

Calculate the annual rates in2014.
Annual rates (2014)=$20800times(+.025)6=$23457.64Annual\, rates\, (2014) = \$20800 \\times ( +.025)^{6} = \$23457.64Since the question asks for the answer to the nearest dollar, we can round this to $23458.
The owner should pay $23458 in annual rates in2014.

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