Question

Problem 1.11 Suppose an initial investment of $100 grows according to the accumulated amount function A(t) 100(1 0.05t) (t20). (a) Find the effective rate of interest earned during the 5th year is (b) Find the force of interest δ(t). (c) Find the "average rateequivalent annual effective rate) of interest earned during the first five years.

Answer 1

a)As a reminder: it+1= [A(t+1) – A(t)]/A(t)

At the end of year 5, i5= [A(5) – A(4)]/A(4)100[(1.05) – (1.04)]/100(1.04) => i5= 0.009615

b)

Effective rate of discount d = 1-v. a. => v= 0.9905 and d = 0.0095.

c). δ = ln (1.009615) = 0.009569.

d.)

By the end of year 5, the fund has grown to 1.05.The question doesn’tspecify that we want the equivalent compound rate, compounded annually,but that is the natural interpretation. The equivalent annual rate,compounded annually, is 1.051/5= 1.009806. So the rate is 0.009806.