Question

During the recent recession, Bob's home value dropped to only $175,000. Since then the economy has turned around and the market is improving at a rate of 4.5% annually. At this rate, how much will Bob's home be worth 12 years after the market started improving? And what equation did you use?

Answer 1

Bob's home will worth $296,779.25 after 12 years.

Equation used is
`FV = $175,000( 1 + 4.5/100)^(12)\\`

Explanation:

Current value of Bob's house =
`FV = $175,000( 1 + 4.5/100)^12\\FV = $175,000( (100+ 4.5)/100)^12\\FV = $175,000( (104.5)/100)^12\\FV = $296,779.25`

market is improving at 4.5% annually.

This, means that the value of house gets appreciated by 4.5% each year from its previous year value.

This is a problem of compound interest formula

`FV = PV(1+r/100)^n`

where PV is the present value of any thing

FV is the future value

r is the annual rate of interest

t is the time in number of year for which rate is applicable.

_____________________________________

Given

PV = $175,000.

r = 4.5%

t = 12 years

Value after 12 year will be given by

`FV = $175,000( 1 + 4.5/100)^(12)\\FV = $175,000( (100+ 4.5)/100)^(12)\\FV = $175,000( (104.5)/100)^(12)\\FV = $296,779.25`

Thus, Bob's home will worth $296,779.25 after 12 years.

Equation used is
`FV = $175,000( 1 + 4.5/100)^(12)\\`