An investment account was initiated with an investment of $1000. The fund had grown to $1200 after one year, and an additional $1000 was invested. The fund balance at the end of two years was $2200.

(a) What annual effective interest rate was earned in the first year? What annual effective interest rate was earned in the second year?

(b) What was the equivalent time-weighted annual effective interest rate for the two years?

(c) What equivalent annual effective interest rate was earned for the two years? (This is the dollar-weighted yield rate.) Calculate it exactly and also using the simple interest approximation.

(d) Explain why the answer in (c) is smaller than the answer in (b)