Question

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?

Answer 1

she should save it for minimum 9.1 years.

Step-by-step explanation:

• compound interest formula:
  `\sf A = P(1+(r)/(100) )^n`

• where A is money earned, P is investing money, r is rate of interest, n is time.

solve:

`\hookrightarrow \sf 12700 =8000 (1+(5.25)/(100) )^n`

change sides

`\hookrightarrow \sf (12700)/(8000) = (1+(5.25)/(100) )^n`

take ln on both sides

`\hookrightarrow \sf n\ln \left(1+(5.25)/(100)\right)=\ln \left((127)/(80)\right)`

simplify

`\hookrightarrow \sf n=(\ln \left((127)/(80)\right))/(\ln \left((105.25)/(100)\right))`

final answer

`\hookrightarrow \sf n=9.03216`

rounding to nearest tenth

`\hookrightarrow \sf n=9.1`