Consider a fully continuous 15-pay whole life insurance of 10,000 on a life aged 20.

(i) Write down the prospective benefit reserve formula at time t. 

(ii) The force of mortality is 0.03 in the first 10 years and 0.06 thereafter, and the force of interest is 0.05. Calculate, to the nearest integer, the benefit reserve at time 13 for the insurance.

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