vannettashelton vannettashelton
  • 10-05-2017
  • Mathematics
contestada

A loan of $47,000 is made at 4.5% interest, compounded annually. After how many years will the amount due reach $63,000 or more?

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apologiabiology
apologiabiology apologiabiology
  • 10-05-2017
[tex]A=P(1+r)^t[/tex] is comounded yearly  formula

rat ie 4.5%
P=47000
solve for when A=63000



[tex]63000=47000(1+0.045)^t[/tex]
divide both sides by 47000
[tex] \frac{63}{47} =(1.045)^t[/tex]
take the ln of both sides
[tex] ln(\frac{63}{47}) =ln((1.045)^t)[/tex]
[tex] ln(\frac{63}{47}) =t(ln(1.045)[/tex]
divide both sides by ln(1.045)
[tex] \frac{ln(\frac{63}{47})}{ln(1.045)}=t [/tex]
using calculator
6.656=t
so after about 6.7 years
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