Yutong Trading (YUT) sells variable annuity contracts embedded with guaranteed minimum maturity benefit (GMMB) riders to policyholders approaching retirement. A variable annuity contract is structured as a contract between the policyholder and YUT under which the policyholder makes a single premium payment at the start of the contract. In return, YUT guarantees minimum guaranteed return of 3.5% per annum as long as the contract is still in force. At initial time, t = 0, the policyholder makes a premium payment of P of which P x% is deducted by YUT as insurance charges associated with providing the guarantees embedded in the variable annuity contract. The net premium after deducting insurance charges is invested in a fund whose return is indexed to the performance of the main benchmark index whose level at initial time is S0.

Upon maturity of the variable annuity contract at time, T, YUT will pay the policyholder

You are also given the following information:

(i) The contract matures in 5 years.

(ii) Dividends are not incorporated in the benchmark index. That is, the index is constructed so that stock dividends are not reinvested.

(iii) The continuously compounded dividend yield of the index is 5% per annum.

(iv) The initial index level is S(0) = 100.

(v) The price of a 5-year European put option on the benchmark index with strike price of $135 is $27.50.

(vi) The continuously compounded risk-free rate of interest is 3% per annum.

Determine x% such that YUT breaks even, that is, does not make or lose money on this variable annuity contract.

P(1 %) s() S(0) ? 1.0357 P(1 %) s() S(0) ? 1.0357