1. If the accumulation function is a(t) = 1 + 0.05t², where t is measured in years, find the effective interest rate i_n for year n.

2. Suppose the effective interest rate over years 4 and 5 is i_[3,5] = 0.05, that A(5) = 2100, and that A(2) = 1923. Find i₃.

3. Suppose an accumulation function is given by

a(t) = t² + t + .

(a) Find .

(b) If $1,000 accumulates to $1,200 after two years, and $500 accumulates to $3,800 after three years, find and .

(c) What is a(1)? Why can this not actually be an accumulation function?

4. A loan is made at a simple interest rate of 5% per year. In which year will the effective interest rate be 2.5%?

5. An amount $1,200 is invested and earns 2% effective interest per year. After T years the balance is $1,406. Find T.

6. $900 is deposited into an account which pays effective interest i per year. After 17 years, the balance in the account is $3,330. Find i.

7. Mahmoud borrows $2,000 for one year, at an annual effective discount rate of 3%. How much money does he gain right now?

8. Neha borrows $1,100 at a discount rate of D. She has $1,067 to spend right now. What is the discount rate, and what interest rate is it equivalent to?

9. Explain why, if the accumulation function a(t) is increasing, then d_n i_n for every n. 10. Suppose d_[3,5] = 3.7% and d₃ = 1.2%. Find i_[2,5].