Suppose that $18,000 is invested in a bond fund and the account grows to $23,344.74 in 5 yr. a. use the model a = pert to determine the average rate of return under continuous compounding. round to the nearest tenth of a percent. b. how long will it take the investment to reach $30,000 if the rate of return continues? round to the nearest tenth of a year

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.

the entire expression should be subtracted from 30. to subtract the quantity, distribute the negative sign, which changes the signs on the terms. so, the –2 changes to positive and gets added to 30 instead of subtracted from it.

hope this ! ^w^

(8+64)^2= 5184 < answer

step-by-step explanation:

2^3 = 8

4^3= 64

(8+64)^2 = 5184