Today I went to the East mall. After exiting the Bukit Kecil MTR station, I was approached by a friendly investment consultant from Avenda Insurance, who recommended me to subscribe to the following investment plan. The plan requires me to invest \(\$ 3,581\) per year over the first 10 years. No contribution is required from year 11 until year 20, and the total projected surrender value is \(\$ 50,862\) at maturity \(N=20\). The plan also includes a death benefit which is not considered here.

a) Using the following graph, compute the constant interest rate over 20 years corresponding to this investment.

b) Compute the projected value of the plan at the end of year 20, if the annual interest rate is \(r=3.25 \%\) over 20 years.

c) Compute the projected value of the plan at the end of year 20, if the annual interest rate \(r=3.25 \%\) is paid only over the first 10 years. Does this recover the total projected value \(\$ 50,862\) ?