Answer:
a. 5.2%
b. 9.8 years
Step-by-step explanation:
a. Put the given numbers in the formula and solve for r.
... 23,344.74 = 18,000×e^(r·5)
... 23,344.74/18,000 = e^(5r) . . . . . divide by 18000
... ln(1.29693) = 5r . . . . . . . . . . . . . . take the natural logarithm
... 0.26/5 = r = 0.052 = 5.2% . . . . . divide by 5
The rate of return is 5.2%, compounded continuously.
b. Put the given numbers in the formula and solve for t.
... 30,000 = 18,000×e^(0.052t)
... 30,000/18,000 = e^(0.052t) . . . . . divide by 18,000
... ln(5/3) = 0.052t . . . . . . take the natural log
... 0.510826/0.052 = t = 9.8 . . . . . divide by the coefficient of t
It will take 9.8 years for the investment to reach $30,000.
