Question

Be sure to show all of your work in the space provided. Your answers should be correct to 3 places after the decimal point. 1. Betty and Bob invest $10,000 for 5 years resulting in an account balance of $15,000. a. Algebraically find their per annum simple rate of return. b. Algebraically find their effective rate of return. c. Algebraically find their per annum continuous rate of return.

Answer 1

Amount Invested = P = $10000

Number of Years = n = 5

Future Value = F = $15000

(a) Let Simple Rate of Return be r

=> F = P + Prn

=> 15000 = 10000 + 10000*r*5

=> r = (15000 - 10000)/(10000*5) = 0.10 = 10%

(b) Let the Effective Rate of Return be r

=> F = P(1+r)ⁿ

=> r = (F/P)^1/n - 1 = (15000/10000)^1/5 - 1 = 0.0845 or 8.45%

(c) Let continuous rate of return be r

=> F = Pe^rn

=> r = (1/n)*ln (F/P) = (1/5)*ln (15000/10000) = 0.0811 or 8.11%