0 0 Arnold imports invest $400,000 at 8% p.a simple interest

Question

1) How many years will it take for the investment to triple in value?
2) How much is the investment worth if it triples in value?
3) How much interest is earned?
4) Calculate the time for the investment to triple in value

Please show working
Thanks

Answer 1

For simple interest       I = Prt

I = interest earned

r = interest rate =.08

t = time in years

 

1)  If the investment triples in value we want the investment to total

     3(400,000) = $1,200,000     Note:  This is the answer to part 2.

     If we start with 400,000 and end with 1,200,000 our interest earned

     is 1,200,000 - 400,000 = $800,000    Note:  This is the answer to part 3

 

 

     Our I = Prt  is now  800,000 = 400,000(.08)t

     t = 800,000/(400,000(.08)) = 2/.08 = 25 years

 

2)  $1,200,000 as noted above

 

3) $800,000 as noted in part 1

 

4)  This is the same question as part 1.... 25 years

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If this was compound interest instead of simple interest our

formula would be   A = P(1+r/n)^nt

Where A = final amount

          P = principal = 400,000

          r = interest rate = .08

          n =  # times compounded per year = 1 for annual

          t = time in years

 

We want to know how long until the investment triples ...or A=3P

3P = P(1+.08/1)^1(t)

3 = 1.08^t

log 3 = log 1.08^t

log 3 = t(log 1.08)

t = (log 3)/(log 1.08) ≅ 14.3 years

 

The investment would triple in value in 14.3 years if this was compound interest