MISCELLANEOUS EXERCISE - 2 -Solve the following problems.1. A house valued at Rs. 8,00,000 is insured at 75% of its value. If the rate of premium is 0.80 %. Find the premium paid by the owner of the house. If agent's commission is 9% of the premium, find agent's commission.2. A shopkeeper insures his shop and godown valued at Rs.5,00,000 and Rs.10,00.000 respectively for 80 % of their values. If the rate of premium is 8 %, find the total annual premium.3 A factory building is insured for (5 /6) th of its value at a rate of premium of 2.50%. If the agent is paid a commission of Rs.2812.50, which is 7.5% of the premium, find the value of the building.4. A merchant takes fire insurance policy to cover 80 % of the value of his stock. Stock worth Rs.80,000 was completely destroyed in a fire. while the rest of stock was reduced to 20% of its value. If the proportional compensation under the policy was Rs.67,200, find the value of the stock.5. A 35-year old person takes a policy for Rs.1,00,000 for a period of 20 years. The rate of premium is Rs.76 and the average rate of bonus is Rs.7 per thousand p.a. If he dies after paying 10 annual premiums, what amount will his nominee receive?6. 15,000 articles costing Rs.200 per dozen were insured against fire for Rs.1,00,000. If 20 % of the articles were burnt completely and 2400 of other articles were damaged to the extent of 80% of their value, find the amount that can be claimed under the policy.7. For what amount should a cargo worth Rs.25,350 be insured so that in the event of total loss, its value as well as the cost of insurance may be recovered when the rate of premium is 2.5 %.8. A cargo of grain is insured at (3/4) % to cover 70% of its value. Rs.1,008 is the amount of premium paid. If the grain is worth Rs. 12 per kg, how many kg of the grain did the cargo contain?9. 4000 bedsheets worth Rs.6,40,000 were insured for (3/7) th of their value. Some of the bedsheets were damaged in the rainy season and were reduced to 40% of their value. If the amount recovered against damage was Rs.32,000. find the number of damaged bedsheets.10. A property valued at Rs.7,00,000 is insured to the extent of Rs.5,60,000 at (5/8) % less 20%. Calculate the saving made in the premium. Find the amount of loss that the owner must bear, including premium, if the property is damaged to the extent of 40 % of its value.11. Stocks in a shop and godown worth Rs.75,000 and Rs.1,30,000 respectively were insured through an agent who receive 15% of premium as commission. If the shop was insured for 80% and godown for 60% of the value, find the amount of agent’s commission when the premium was 0.80% less 20%. If the entire stock in the shop and 20% stock in the godown is destroyed by fire, find the amount that can be claimed under the policy.12. A person holding a life policy of Rs.1,20,000 for a term of 25 years wants to discontinue after paying premium for 8 years at the rate of Rs.58 per thousand p. a. Find the amount of paid up value he will receive on the policy. Find the amount he will receive if the surrender value granted is 35% of the premiums paid, excluding the first year's premium.13. A godown valued at Rs.80,000 contained stock worth Rs. 4,80,000. Both were insured against fire. Godown for Rs.50,000 and stock for 80% of its value. A part of stock worth Rs.60,000 was completely destroyed and the rest was reduced to 60% of its value. The amount of damage to the godown is Rs. 40,000. Find the amount that can be claimed under the policy.14. Find the amount of an ordinary annuity if a payment of Rs. 500 is made at the end of every quarter for 5 years at the rate of 12% per annum compounded quarterly.15. Find the amount a company should set aside at the end of every year if it wants to buy a machine expected to cost Rs.1,00,000 at the end of 4 years and interest rate is 5% p. a. compounded annually.16. Find the least number of years for which an annuity of Rs. 3,000 per annum must run in order that its amount exceeds Rs. 60,000 at 10% compounded annually. [(1.1)11 = 2.8531, (1.1)12 = 3.1384]17. Find the rate of interest compounded annually if an ordinary annuity of Rs. 20,000 per year amounts to Rs. 41,000 in 2 years.18. A person purchases a television by paying Rs.20,000 in cash and promising to pay Rs. 1000 at end of every month for the next 2 years. If money is worth 12% p. a., converted monthly. find the cash price of the television.19. Find the present value of an annuity immediate of Rs. 20,000 per annum for 3 years at 10% p.a. compounded annually.20. A man borrowed some money and paid back in 3 equal installments of Rs.2160 each. What amount did he borrow if the rate of interest was 20% per annum compounded annually? Also find the total interest charged.21. A company decides to set aside a certain amount at the end of every year to create a sinking fund that should amount to Rs. 9,28,200 in 4 years at 10% p.a. Find the amount to be set aside every year.22. Find the future value after 2 years if an amount of Rs. 12,000 is invested at the end of every half year at 12% p. a. compounded half yearly.23. After how many years would an annuity due of Rs. 3.000 p.a. accumulated Rs.19.324.80 at 20% p. a. compounded half yearly? [Given (1.2)4 = 2.0736]24. Some machinery is expected to cost 25% more over its present cost of Rs. 6,96,000 after 20 years. The scrap value of the machinery will realize Rs.1,50,000. What amount should be set aside at the end of every year at 5% p.a. compound interest for 20 years to replace the machinery? [Given (1.05)20= 2.653]