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Assume in a certain city that housing costs have been increasing at 5.2% per year compounded annually for the past 8 years. A house worth $260,000 today would have had what value 8 years ago?

Respuesta :

calculista

Answer:

[tex]\$173,319.50[/tex]  

Step-by-step explanation:

we know that    

The compound interest formula is equal to  

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

[tex]t=8\ years\\ A=\$260,000\\ r=5.2\%=5.2/100=0.052\\n=1[/tex]  

substitute in the formula above

[tex]260,000=P(1+\frac{0.052}{1})^{1*8}[/tex]  

solve for P

[tex]260,000=P(1.052)^{8}[/tex]  

[tex]P=260,000/(1.052)^{8}=\$173,319.50[/tex]  

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