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A person invests 8500 dollars in a bank. The bank pays 6% interest compounded semi-annually. To the nearest tenth of a year, how long must the person leave the money in the bank until it reaches 15500 dollars?

A person invests 8500 dollars in a bank The bank pays 6 interest compounded semiannually To the nearest tenth of a year how long must the person leave the money class=

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samuelonum1

The time required to get a total amount of $15,500.00 with compounded interest on a principal of $8,500.00 at an interest rate of 6% per year and compounded 2 times per year is 10.162 years (about 10 years 2 months)

Compound Interest Analysis

Given Data

  • Principal P = $8,500
  • Rate  r = 6%
  • Final Amount A = $15500
  • Time t  = 1 year

Calculation Steps:

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

r = R/100

r = 6/100

r = 0.06 per year,

Then, solve the equation for t

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

t = ln(15,500.00/8,500.00) / ( 2 × [ln(1 + 0.06/2)] )

t = ln(15,500.00/8,500.00) / ( 2 × [ln(1 + 0.03)] )

t = 10.162 years

Learn more about compound interest here:

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