IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Key assurance and annuity contracts
A whole life policy on a life aged 60 pays a sum assured of Rs 8,00,000 at the end of the year of death. A single premium is paid at outset. At rate i the value of A60 is 0.5000 and the value of the whole life annuity-due a60 is 11.50. The same policy is instead financed by level annual premiums payable in advance for life. What is the annual net premium?
Equate the expected present value of premiums to that of benefits: P x 11.50 = 8,00,000 x 0.5000 = 4,00,000. So P = 4,00,000 divided by 11.5, giving an annual net premium of Rs 34,782.61.
- ARs 34,782.61Correct
- BRs 69,565.22
- CRs 4,00,000.00
- DRs 47,000.00
- Rs 27,826.09
Explanation
Net premium P satisfies P x a60 = 8,00,000 x A60. So P = 8,00,000 x 0.5 / 11.5 = 4,00,000 / 11.5 = 34,782.61. Option 1 doubles it, and option 2 is the single premium.
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