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HW3: Problem 15 Previous Problem Problem List Next Problem (1 point) (Exercise 2.12) Fund A accumulates at a rate of 10% convertible monthly. Fund B accumulates with a force of interest 8, = 0.19t. At time t = 0 equal deposits are made in each fund. Find the next time that the two funds are equal. ANSWER = 1.25688 years. Preview My Answers Submit Answers

Answer 1

The equivalent annual effective rate of interest for fund A

Ra= (1+0.1/12)^12 -1 = 0.1047131 or 10.47%

The equivalent annual effective rate for Fund B (Rb) can be found by first calculating the accumulation function

A(t) = expl/0.19tdi Jo

=> A(t) = exp ( 0.19/2 t²)^t₀ = Exp ( 0.095 t²)

So, (1+Rb) ^t = Exp (0.095t²)

=> 1+Rb = Exp (0.095t)

=> Rb = Exp (0.095t) - 1

If Fund A and Fund B are to be equivalent , Ra and Rb should be equal

So, Exp (0.095t) - 1 = 0.1047131

=> 0.095t = ln (1.1047131) = 0.0995856

=> t = 1.0482698

So, the two funds will give same value after 1.042698 years