Suppose that 10000 is invested in a bond fund and the accoun

Suppose that $10,000 is invested in a bond fund and the account grows to $13, 915.23 in 4 yr. a. Use the model A = Pe^rt to determine the average rate of return under continuous compounding. Round to the nearest tenth of a percent. Avoid rounding in intermediate steps. b. How long would it take the initial investment to reach $25,000 if the rate of return continues? Round to 1 decimal place. Round values in intermediate steps. a. The average rate of return under continuous compounding is approximately %.

Solution

A = 13915.23 ; P = 10,000

t = 4 yrs

13915.23 = 10,000e^(r*4)

take natural log on both sides:

ln(13915.23/10,000) = 4r

a) r = 0.0826 = 8.26 = 8.3% ( avg rate of return)

b) A = 25000 ; t = ?

So, 25000 = 10,0000e^(0.0826*t)

t = 11.093 yrs