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Shen deposited $5000 into an account with a 6.4% annual interest rate, compounded quarterly. Assuming that no withdrawals are made, how long will it take for the investment to grow to $6145 ?

Do not round any intermedlate computations, and round your answer to the nearest hundredth.

User Saeta
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1 Answer

3 votes

We can use the compound interest formula to solve this problem:


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

Where:

  • A = the future value of the investment ($6145)
  • P = the initial deposit ($5000)
  • r = annual interest rate (6.4% or 0.064)
  • n = number of times interest is compounded per year (quarterly, so 4)
  • t = number of years

Substituting the given values into the formula:


6145=5000(1+(0.064)/(4) )^(4t)

Now, we need to solve for t. Divide both sides by 5000 and then take the natural logarithm (ln) of both sides:


ln((6145)/(5000) ) = 4tln (1+(0.064)/(4))

Now, isolate t by dividing both sides by
4 ln (1+(0.064)/(4) ):


t=(ln(6145)/(5000) )/(4ln(1+ (0.064)/(4) ))

Now, plug in the values and calculate:


t = (0.201943)/(4⋅0.015760) = 3.18

Rounded to the nearest hundredth, it will take approximately 3.18 years for the investment to grow to $6145.

User DieterDP
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