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A person invests 4000 dollars in a bank. The bank pays 5.5% interest compounded annually. To the nearest tenth of a year, how long must the person leave the money in the bank until it reaches 5600 dollars?

A=P(1+r/n)^nt

Sagot :

nuhulawal20

if the person leaves the money in the bank, the time it will take for it to reach the given final amount is 6.3 years.

What is an interest in banking?

Interest is simply the amount of money a lender or financial institution receives for lending out money or pays for receiving money.

The formular for calculating compound interest is expressed as;

A = P(1 + r/n)^(n*t)

Where A is final amount, P is initial principal balance, r is interest rate, n is  number of times interest applied per time period and t is number of time periods elapsed.

Given the data in the question;

  • Initial principal balance P = $4000
  • Interest rate r = 5.5% anuually = 5.5/100 = 0.055
  • Final amount A = $5600
  • Time t = ?

We substitute our given values into the expression above.

A = P(1 + r/n)^(n*t)

5600 = 4000(1 + 0.055/1)^(1*t)

5600 = 4000( 1.055 )^t

( 1.055 )^t = 5600 / 4000

( 1.055 )^t  = 1.4

We take log of each sides

0.02325t = 0.1461

t = 0.1461 / 0.02325

t = 6.3

Therefore, if the person leaves the money in the bank, the time it will take for it to reach the given final amount is 6.3 years.

Learn more about compound interest here: https://brainly.com/question/27128740

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