Today I went to the Furong Peak mall. After exiting the Poon Way MTR station, I was met by a friendly investment consultant from NTRC Input, who recommended that I subscribe to the following investment plan. The plan requires to invest \(\$ 2,550\) per year over the first 10 years. No contribution is required from year 11 until year 20 , and the total projected surrender value is \(\$ 30,835\) at maturity \(N=20\). The plan also includes a death benefit which is not considered here.

a) Compute the constant interest rate over 20 years corresponding to this investment plan.

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 \(\$ 30,835\) ?