Answered

From personal advice to professional guidance, IDNLearn.com has the answers you seek. Find reliable solutions to your questions quickly and accurately with help from our dedicated community of experts.

A person invests 8000 dollars in a bank. The bank pays 5.25% interest compounded annually. To the nearest tenth of a year, how long must the person leave the money in the bank until it reaches 12700 dollars?

Sagot :

Fieryanswererftidn

Answer:

she should save it for minimum 9.1 years.

Explanation:

  • compound interest formula: [tex]\sf A = P(1+\dfrac{r}{100} )^n[/tex]
  • where A is money earned, P is investing money, r is rate of interest, n is time.

solve:

[tex]\hookrightarrow \sf 12700 =8000 (1+\dfrac{5.25}{100} )^n[/tex]

change sides

[tex]\hookrightarrow \sf \dfrac{12700}{8000} = (1+\dfrac{5.25}{100} )^n[/tex]

take ln on both sides

[tex]\hookrightarrow \sf n\ln \left(1+\dfrac{5.25}{100}\right)=\ln \left(\dfrac{127}{80}\right)[/tex]

simplify

[tex]\hookrightarrow \sf n=\frac{\ln \left(\dfrac{127}{80}\right)}{\ln \left(\dfrac{105.25}{100}\right)}[/tex]

final answer

[tex]\hookrightarrow \sf n=9.03216[/tex]

rounding to nearest tenth

[tex]\hookrightarrow \sf n=9.1[/tex]

We value your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Your search for solutions ends at IDNLearn.com. Thank you for visiting, and we look forward to helping you again.