If $20,000 is invested at an interest rate of 2% per year, compounded semiannual

label Algebra
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If $20,000 is invested at an interest rate of 2% per year, compounded semiannually, find the value of the investment after the given number of years. (Round your answers to the nearest cent.)
(a)     6 years
  

(b)     12 years
  

(c)     18 years
 
Jul 17th, 2015

Thank you for the opportunity to help you with your question!

We just need to use the following expression:

FV = PV(1 + (i/n) )^(n*t)

n is the times that is compounded (if it is semiannual then n = 2)

t is the number of periods (number of years)

i is the interest rate in decimal form

PV is the initial value or initial investment

FV is the future value (what we need to find)

Part a

So we would have:

PV = $20,000   ;   i = 2% = 0.02   ;   n = 2    ;  t = 6 years

FV = (20,000)(1 + (0.02/2) )^(2*6) = (20,000)(1 + 0.01)^12 = (20,000)(1.01)^12 = 22536.5006

FV = $22536.50

Part b

t = 12 years

FV = (20,000)(1 + (0.02/2) )^(2*12) = (20,000)(1 + 0.01)^24 = (20,000)(1.01)^24 = 25394.69297

FV = $25394.69

Part c

t = 18 years

FV = (20,000)(1 + (0.02/2) )^(2*18) = (20,000)(1 + 0.01)^36 = (20,000)(1.01)^36 = 28615.37567

FV = $28615.38

Please let me know if you need any clarification. I'm always happy to answer your questions.
Jul 17th, 2015

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