Insurance and Annuity

Ex. No. 1.
1.  Find the premium on property worth Rs. 12,50,0000 at 3% if (i) the property is fully insured (ii) the property is insured to the extent of 80%  of its value.
2. A shop is valued at Rs. 2,40,000 for 75% of its value. If the rate of premium is 90 paise percent, find the premium paid by the owner of the shop. if an agent gets commission at 15% of the premium, find the agent’s commission.
3. A person insures his office valued at Rs. 2,00,000 for 80% of its value. He pays Rs. 5,000 as premium. Find the rate of premium. If the agent gets commission at 11%, find his commission.
4. A building is insured for 80% of its value. The annual premium at 70 paise percent amounts to Rs. 2800. Fire damaged the building to the extent of 60% of its value. How much can be claimed under the policy?
5. Stock worth Rs. 3,75,000 was insured for Rs. 2,25,000. Stock worth Rs. 1,50,000 was burnt completely due to fire and the balance was reduced to 75% of its value. What sum can be claimed under the policy.
6. A cargo of rice was insured at 5/8% to cover 80% of its value. The premium paid was Rs. 5250. If the rice was worth Rs. 21 per kilo, how many kilos of rice did the cargo contain?
7. 30000 articles costing Rs. 200 per dozen were insured against fire for Rs. 1.20 lakh. If 20 % of the articles were completely burnt and another 3600 articles were damaged to 80% of their value, find the amount that can be claimed under the policy.
8. For what amount should a cargo worth Rs. 87,525 be insured so that in the event of total loss, its value as well as the cost of insurance may be recovered, the rate of premium being Rs. 2 percent and other expenses 75 paise percent.
9. A person takes out three policies with different insurance companies on an estate valued at Rs. 2,00,000. The amount insured with each company is as follows.
Amount insured
Rs. 80000
Rs. 50000
Rs. 70000
Find the amount recoverable from each company in the event of loss to the extent of Rs. 4,500.
10. A car valued at Rs. 4,00,000 is insured for Rs. 2,50,000. The rate of premium is 5% less 20%. How much loss does the owner bear including the premium, if value of the car is reduced to 60% of its original value?
11. Stocks in a shop and godown costing Rs. 50,000 and Rs. 1,00,000 respectively were insured through an agent who was paid 12% of the total premium. If the former was insured for 80% and the latter for 60% of the value, find the agent’s commission, when the rate of premium was 80 paise percent less 20%.
12. The rate of premium on a policy of Rs. 50,000 is Rs. 56 per thousand per annum. A rebate of 75 paise per thousand is allowed when the premiums are paid annually. Find the net amount of premium payable if the policyholder pays annually.
13. A warehouse valued at Rs. 10,000 contained goods worth Rs. 60,000. the warehouse was insured against fire for Rs. 4,000 and the goods to the extent of 90% of their value. A fire broke out and goods worth Rs. 20,000 were completely destroyed, while the remainder was damaged and reduced to 80% of its value. The damage to the warehouse was to the extent of Rs. 2000. Find the total amount that can be claimed.
14. A person takes a life policy for Rs. 80,000 for a period of 20 years. he pays premium for 10 years during which bonus was declared at the average rate of Rs. 20 per year per thousand. Find the paid up value of the policy, if he discontinues paying the premium after 10 years.
EX. NO. 2.
1. Find the accumulated (future) value of annuity of Rs. 400 made annually for 3 years at interest rate 8% compounded annually. [Given (1.08)3 = 1.2597]
2. Mr. Godbole invested Rs. 2000 at the end of each year in a finance company that offered him interest compounded at 10% p.a. What is the amount accumulated at the end of 4 years? [Given (1.1.)4 = 1.4641]
3. Find the amount accumulated after 2 years if sum of Rs. 12, 000 is invested at the end of every 6 months at 12% p.a. compounded half yearly. [Given (1.06)4 = 1.2625]
4. Find the accumulated value after 1 year of an annuity immediate in which Rs. 20,000 are invested every quarter, at 16 % p.a. compounded quarterly. [Given (1.04)4 = 1.1699]
5. Find the present value of an annuity immediate of Rs. 18,000 p.a. for 3 years at 9% p.a. compounded annually. [Given (1.09)-3 = 0.7722]
6. Find the present value of an ordinary annuity of Rs. 42,000 per annum for 4 years at 14% p.a. compounded annually. [Given (1.14)-4 = 0.5921]
7. Mrs. Menon Plans to save for her daughter’s marriage. She wants to accumulated a sum of Rs. 4,00,000 at the end of 4 years. How much should she invest at the end of each year from now, if she can get interest compounded at 10% p.a.?  [Given (1.1.)4 = 1.4641]
8. Mr. Chitale wishes to create a fund of Rs. 5 lakhs after 4 years when he retires. He decides to set aside a sum of money at the end of each coming year for the same, investing it in a bank giving him 10% p.a. compounded annually. What sum should be kept aside each year?  [Given (1.1.)4 = 1.4641]
9. Find the rate of interest compounded per annum if an annuity immediate at Rs. 10000 per year amounts to Rs. 130000 in 3 years.
10. Find the number of years for which an annuity of Rs. 200 is paid at the end of each year, if its accumulated amount works out to be Rs. 662 with interest compounded at 10% p.a.?
11. Find the accumulated value of annuity due of Rs. 500 p.a. for 3 years at 10 % p.a. compounded annually. [Given (1.1.)= 1.331]
12. A person plans to put Rs. 200 at the beginning of each year for 2 years in a deposit giving 2% p.a. compounded annually. What will be the accumulated amount after 2 years?
13. Find the present value of an annuity due of Rs. 400 to be paid per quarter, at 32% p.a. compounded quarterly for 1 year. [(1.08)-4 =0.7350]
14. An annuity immediate is to be paid for certain number of years, at 12% p.a. It’s present value is Rs. 5000 and the accumulated value is Rs. 10,000.  Find the amount of each annuity payment?
15. For an annuity immediate paid for 3 years with interest compounded at 10% p.a. the present value is Rs. 12000. What is its accumulated value after 3 years? [Given (1.1.)= 1.331]
16. A person sets up a sinking fund in order to have Rs. 10 lakh after 10 years for his children’s education. How much amount should be set aside bi-annually into an account paying 5% p.a. compounded semi - annually.? [Given (1+0.025)20 = 1.675]