Question

Problem 1.8 You deposit $5,000 in an account earning 5% interest compounded semi-annually for 2 years and 7% interest compounded quarterly thereafter. What is the account value after 7 years? Problem 1.9 What is the equivalent effective annual (compound) interest rate in Problem 1.8? Problem 1.10 You deposit $5,000 in an account that earns 5% interest compounded annually in years 1 and 2, and thereafter a continuous rate δ(t) = 2/(t + 1) (t > 0). What is the value of the account after 5 years? 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 rate" equivalent annual effective rate) of interest earned during the first five years.

Answer 1

Problem 1.8

Amount deposited = 5,000

Interest = 5% compounded semi annually

Time =2 years

Interest rate = 7% compounded for 5 years quarterly

Value after 7 years = 5000*(1+0.05/2)^4 *(1+0.07/4)^20

Value after 7 years = $7,808.25

Problem 1.9

Equivalent annual compound interest = (7808.25/5000)^(1/7) -1 = 6.57%

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