Annuity Problems Solutions

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Annuity Problems 1. As a winner of a breakfast cereal competition, you can choose any of the following prizes, using an interest rate of 12%: a. $ 100,000 now b. $ 180,000 at the end of five years 180,000/(1.12)^5 = 180,000*.567 = 102060 c. $ 11,400 a year forever 11400/.12 = 95000 d. $ 19,000 for each of 10 years with payments made at the end of the year 19000 * PVIFA 10,12% = 19000 * 5.65= 107,350 e. $ 19,000 for each of 10 years with the payment made at the beginning of the year Normal annuity * 1.0r = 1,07,350* 1.12 = 120,232 2. You wish to accumulate Rs 80,00,000 by the end of 5 years by making equal annual yearend deposits over the next 5 years. Assuming 7 per cent rate of return, how much should you deposit at the end of each year to accumulate Rs 80,00,000? A*FVIFA = 80,00,000 A * 5.751 = 80,00,000 A = 13,91,062 3. An investor is 50 years of age today. He will retire at the age of 60. In order to receive Rs 2,00,000 annually for 10 years after retirement, how much amount should he have at the time of retirement? Assume the required rate of return is 10 per cent. 200,000 * PVIFA(10,10%) = 200,000 * 6.145 = 12,29,000 4. You want to borrow Rs 15,00,000 to buy a flat. You approach a housing company which charges 13% interest. You can pay Rs 200,000 per year towards loan amortization. What should be the maturity period of the loan. 200,000 * PVIFA = 15,00,000 PVIFA = 7.5 (30 years) 5. A person gets Rs.20,00,000 on retirement at the age of 60 years. He invests the same in a scheme earning interest at 8% per annum. He decides to withdraw Rs.2,40,000 every year for his domestic expenses. How many years will he be able to withdraw the money? What will be the balance at the end of last year? 2,40,000 * PVIFA = 20,00,000 PVIFA = 8.333 Closest factor for 8% is 14 years 8.244 ± Amount consumed 8.244 * 240000

6.

= 19,78,560 balance left 21,440 at the end of 14 years ± 21440 * (1.08)^14

When you start earning at the age of 25 years, you decide to save Rs.70000 each year in Public Provident Fund A/c. with State Bank of India, earning interest at 8% per annum, compounded annually. What will be the amount you be getting at the age of 50 years 70000*FVIFA = 70000*73.106 51,17,420 7. A finance company advertises that it will pay a lump sum of Rs.44650 at the end of 5 years to investors who deposit annually Rs.6000 for 5 years. What is the rate of interest implicit in this offer? 6000 * FVIFA = 44650 FVIFA = 7.4416 app 20% After 10 years from today, Mr X will receive a pension of INR 10000 per annum. The payment will continue for 16 years. How much is the pension worth today if Mr X¶s interest rate is 10 Per cent. Value of pension which for 16 years = 10000* PVIFA 10%,16 = 10000 * 7.824= 78,240 Value today = 78,240/(1.10)^9 = 78240 * .424 Please note the 9 years above for discounting, it is not 10 - follow the diagram below. On a time line ± the payment starts from the 10th year and continues for 16 years. 1 2 3 5 6 7 8 9 10
10K

8.

11
10K

12
10K

13
10K

14 -------26
10K 10K 10K

The annuity has been discounted up to end of the 9th year, not 10th year

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