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A person invests 8500 dollars in a bank. The bank pays 4.25% interest compounded daily. To the nearest tenth of a year, how long must the person leave the money in the bank until it reaches 12100 dollars?

A person invests 8500 dollars in a bank The bank pays 425 interest compounded daily To the nearest tenth of a year how long must the person leave the money in t class=

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What is compound interest?

To calculate the time the person must leave the money in the bank, we use the formula below.

Formula:

  • A = P(1+r/n)[tex]{nt}[/tex]............. Equation 1

The time that the person will leave the money in the bank until it reaches 12100 dollars is 7.9 years.

How to calculate the time?

Given Data

  • Principal, P = $8,500
  • Rate,  r = 4.25%
  • Final Amount A = $12100
  • Time, t  = 1 year

First, convert R as a percent to r as a decimal

r = R/100

r = 4.25/100

r = 0.0425 per year.

Then, solve the equation for t

t = ln(A/P) / n[ln(1 + r/n)]

t = ln(12100/8,500) / ( 2 × [ln(1 + 0.045/2)] )

t = ln(12100/8,500) / ( 2 × [ln(1 + 0.0225)] )

t = In1.4235 / ( 2 × [ln1.0225]

t = 0.35311 / {2 × 0.02225}

t = 7.9 years

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