Q.The premium on a marine insurance policy is ₹9,000, charged at a rate of 1.5% of the sum insured. Find the sum insured (policy value).

Insurance is a contract in which the insurer, in return for a premium, compensates the insured for a specified loss, up to the sum insured (policy value). Premium is proportional to the sum insured: $\text{Premium}=\text{rate}\times\text{sum insured}$, so the sum insured $=\text{Premium}/\text{rate}$ and the rate $=\text{Premium}/\text{sum insured}$. Rates may be quoted as a percentage or per ₹100 / ₹1000 (₹$r$ per ₹100 $=r\%$; ₹$r$ per ₹1000 $=\tfrac{r}{10}\%$). Property, fire and marine cover follow the principle of indemnity (only the actual loss is paid, capped at the sum insured); life insurance pays the full sum assured. A property may be insured for only a fraction $k$ of its value $V$, giving sum insured $=kV$.