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1 Section II Question 6 The earning member of a family aged 35 years expects to earn till next 25 years. He expects an annual growth of 8% in his existing net income of Rs. 5 lakh p.a. If he considers an average investment yield of 6% till his life expectancy of 80 years, what economic value could be ascribed to his life today? Suggested solutions to 3-mark and 4-mark problems contained in the Additional Sample Questions: Insurance Planning (RAIP) and Retirement Planning (RPEB) Current net income 500,000 Rs. p.a. Rate of increase of net income 8% p.a. Investment yield from investing 6% p.a. Number of years the income is expected to continue 25 years Economic value would be the all earnings of future years discounted today at the investment yield. Economic value 15,785,662 Rs. PV((1+6%)/(1+8%)-1,25, ,0,1) Note 1: The Life Expectancy figure of 80 years is redundant here. Note 2: The Real Return formula is used here with 'investment yield' taken in numerator and growth taken in denominator. Alternative method: Future Value of all earnings for 25 years 67,750,019 Rs *(1+6%)*((1+6%)^25-(1+8%)^25)/(6%-8%) Present Value today at the investment yield of 6% 15,785,662 Rs /(1+6%)^25 Section II Question 7 Mr. X has a 25-year endowment policy, the annual premium being Rs. 15,850 for a sum assured of Rs. 12 lakh. He has paid 18 premiums and has Rs. 6,50,000 towards declared bonuses on this policy. He has met his objectives and has sufficient cover and wealth support. He does not wish to continue in the policy. He has the option to either make this policy paid up, or surrender the same at a factor of 75% of the paid up value. If he chooses to surrender, what return he should earn on the surrender value to offset the paid up value, when due? Paid up value of the policy 1,514,000 Rs *18/ Surrender value = 75% of the above paid up value 1,135,500 Rs *75% Remaining term of the policy 7 years Rate to be earned on surrender value to reach paid up 4.20% p.a. RATE(7,0, , ,) CAGR Note: The paid up value would be payable only on due maturity of the policy. Page 1

2 Section II Question 8 A retiree of age 60 wants to enter into the reverse mortgage scheme by mortgaging his self-occupied house which is valued at Rs. 80 lakh. An approved lending institution agrees to provide periodic monthly payments under the scheme considering a loan to value ratio of 80% and at a rate of interest of 13.75% p.a. If the retiree opts for a 15- year term of reverse mortgage, what fixed periodic monthly payments he stands to receive under the scheme? Value of House 8,000,000 Rs. Loan Eligible 6,400,000 Rs *80% Rate of Interest 13.75% p.a. Term 15 years 180 months Monthly payments under reverse mortgage 10,703 Rs. PMT(13.75%/12,180,0, ,1) Note: (1) Calculation: We generally see in mortgage formula, the loan amount is usually considered with negative sign in PV while FV is 'Nil'. In Reverse Mortgage case, the admissible loan amount is taken with negative sign under FV while PV is 'Nil'. Also, 'begin mode' is considered, i.e. '1' for 'type'. (2) The annuity period is 20 years. Though the annuity payment stops after 20 years, the loan is not payable as long as the mortgagor survives. After the death of the mortgagor and his/her surviving spouse, the lending institution sells the house and recovers loan amount with interest and the balance, if any is paid to the heirs. Section II Question 9 A retiree of age 65 has fixed pension of Rs. 15,000 per month. His household expenses have exceeded his pension of late and are Rs. 16,000 per month now. He has approached an approved lending institution under Reverse Mortgage Scheme. He is offered fixed monthly payments for 15 years at a rate of interest of 13.75% on Rs. 64 lakh eligible value of his home. He meets his annual expenses as increased by 6% inflation every year and invests the excess amount from his two fixed annuities, fixed pension and reverse mortgage stream, in an investment yielding 10% p.a. at the end of every year starting from this year onwards. You assess at the end of five years thus accumulated fund against the total liability under Reverse Mortgage and find that. Value of Reverse Mortgage Loan Eligible 6,400,000 Rs. Rate of Interest 13.75% p.a. Term 15 years Monthly payments under reverse mortgage 10,703 Rs. PMT(13.75%/12,180,0, ,1) Fixed pension 15,000 Rs. p.m. Current household expenses 16,000 Rs. p.m. Excess funds available for investment: End of year 1 116,439 Rs. (( )-16000)*12 Household expenses in the 2nd year 16,960 Rs. p.m *(1+6%) Excess funds available for investment: End of year 2 233,001 Rs. (( )-16960)* *(1+10%) Household expenses in the 3rd year 17,978 Rs. p.m *(1+6%) Excess funds available for investment: End of year 3 349,008 Rs. (( )-17978)* *(1+10%) Household expenses in the 4th year 19,056 Rs. p.m *(1+6%) Excess funds available for investment: End of year 4 463,673 Rs. (( )-19056)* *(1+10%) Household expenses in the 5th year 20,200 Rs. p.m *(1+6%) Excess funds available for investment: End of year 5 576,083 Rs. (( )-20200)* *(1+10%) Mortgage Loan and interest outstanding : End of Year 5 926,830 Rs. FV(13.75%/12,5*12,-10703,0,1) Net Liability due to Reverse Mortgage Loan 350,747 Rs Page 2

3 Alternative Method of finding accumulated fund: PV: Fixed annuities (Pension+RM stream) for 5-year period 1,286,147 Rs. [1] PV(10%,5,-( )*12,0,1) PV: Expenses 6% p.a. for 5-year period 892,675 Rs. [2] PV((1+10%)/(1+6%)-1,5,-16000*12,0,1) PV of excess funds to be invested for 4 annual periods 393,472 Rs. [1-2] (Investment of excess funds began at the end of year 1, thus 1st accumulation end of year 2, ----) Accumulation at the end of year 5 576,083 Rs *(1+10%)^4 Section III Question 4 An individual opened PPF account on 1st April The amount outstanding in his account on 31st March 2013 was Rs. 4,93,564. If he had a balance of Rs. 2,45,428 on 31st March 2010, what amount can he withdraw and from which date? Time Rule: Initial subscription date 1-Apr-2007 Year of initial subscription: Expiry of 5 years from the end of FY of initial subscription 31-Mar-2013 Year of withdrawal to be Amount Rule: 1)Balance at the end of 4th FY preceding , i.e. at the end of year or as on 31st March ,428 Rs. 50% of this balance 122,714 Rs. [1] 2)Balance at the end of preceding FY, i.e. as on 31st March, ,564 Rs. 50% of this balance 246,782 Rs. [2] Lower of [1] and [2] 122,714 Rs. From 1st April, 2013 in the year The Rule of Partial Withdrawal from PPF A/c.: Anytime after the expiry of five years from the end of the financial year in which the initial subscription is made, the subscriber can partially withdraw but not more than fifty percent (50%) from the balance that stood to his / her credit at the end of the fourth financial year immediately preceding the year of withdrawal or at the end of the preceding financial year whichever is lower, less the loan amount (if any). Only one withdrawal is allowed per financial year. Page 3

4 Section III Question 5 An annuity product is designed in such a way that it gives first cash flow at 6% of the corpus at the end of first year and thereafter every year in the form of growing annuity at the rate of 5%. If the cash flows are guaranteed for 15 years, what rate of return is obtained on the corpus invested? Suppose the corpus invested is: 100 Rs. Cash flow at the end of first year 6 Rs. Growth in annuity in every subsequent year 5.00% p.a. Guaranteed period of annuity 15 years (-) Corpus invested (100) + Cash flow Year Cash flow Year Cash flow Year Cash flow Year Cash flow Year Cash flow Year Cash flow Year Cash flow Year Cash flow Year Cash flow Year Cash flow Year Cash flow Year Cash flow Year Cash flow Year Cash flow Year IRR 3.04% Alternative Method: Rate of 15 years level annuity of which level payment pre-5% growth is Rs % RATE(15,6/1.05,-100,0,0) Annual Growth of 5% built into this annuity to make it growing annuity of which first payment is Rs % (1+( %))*(1+5%)-1 Section III Question 6 A retiree has accumulated Rs crore towards his retirement corpus. His current monthly household expenses are Rs. 90,000 which he needs inflation adjusted for 30 years. If he considers average inflation to be 5.5% p.a. from now onwards, what rate of return from a 30 year annuity, payable annually and deferred by one year, should meet his goal? (As in the Alternative Solution to Question 5 above) Accumulated corpus for annuity 18,600,000 Rs. Rate of inflation considered 5.50% p.a. Amount of current annual expenses 1,080,000 Rs *12 Period of growing annuity 30 years Rate of return for annuity % p.m. RATE(30, , ,0,0) Annuity return to be targeted 9.76% p.a. ( %)*(1+5.5%)-1 Rate of 30 years level annuity of which level payment pre-5.5% growth is Rs. 1,080,000. Then, Annual Growth of 5.5% built into this annuity to make it growing annuity of which first payment is Rs. 1,080,000. Page 4

5 Section III Question 7 A professional just retired has accumulated Rs. 40 lakh. He invests this corpus in an investment instrument giving return of 8% p.a. His current annual household expenses are Rs. 5 lakh, escalating at inflation of 6% p.a. He would rent out his other fixed property at an expected annual rent of Rs lakh, the rentals increasing at 6% p.a. The balance expenses are met by withdrawing from the invested corpus. The commercial property, currently valued at Rs. 50 lakh, is expected to appreciate at 8% p.a. He expects to sell the property after 15 years to create a fresh corpus for his living expenses. How long the total funds available are expected to last after 15 years? Corpus already accumulated 4,000,000 Rs. Investment rate obtained in deferred instrument 8.0% p.a. Current household expenses 500,000 Rs. p.a. Rate of inflation of expenses 6.0% p.a. Rent receivable from renting office space on retirement 180,000 Rs. p.a. Rate of increase of rentals 6.0% p.a. PV of 6% increasing expenses for 15 years at 8% discount rate 6,112,623 Rs *(1-((1+6%)^15)/((1+8%)^15))/(8%-6%) or PV(1.08/1.06-1,15, /1.06,0,0) PV of 6% increasing rental for 15 years at 8% discount rate 2,200,544 Rs *(1-((1+6%)^15)/((1+8%)^15))/(8%-6%) or PV(1.08/1.06-1,15,180000/1.06,0,0) Drawn from corpus in 15 years 3,912,079 Rs PV of balance corpus (on investing) 87,921 Rs Accumulated investment after 15 years 278,902 Rs *(1+8%)^15 Value of commercial property now 5,000,000 Rs. Increase in value 8.0% p.a. Valuation after 15 years 15,860,846 Rs *(1+8%)^15 Total fresh corpus after 15 years 16,139, Expenses required after 15 years 1,198,279 Rs. p.a *(1+6%)^15 Period up to which this revised corpus would last years NPER(1.08/1.06-1, /1.06, ,0,0) 16 years 9 months Section III Question 8 A retired person has contracted a 20-year immediate annuity plan which provides an annual stream of income, increasing year-on-year at 5%. He is due to receive 5th installment of Rs lakh which is 6% of the balance corpus remaining in annuity. He wants the term of the annuity to increase. He estimates that Rs lakh would be sufficient for his current living expenses. He proposes this to the annuity provider with other terms remaining as originally agreed. If the yield of the annuity is 6.5% p.a., how many more installments would get added in the restructured annuity than the original? 5th cash flow stream to be received 550,000 Rs. % of balance amount 6% The outstanding balance of corpus before 5th installment 9,166,667 Rs /6% Revised withdrawal amount of 5th installment 475,000 Rs. Interest rate 6.50% p.a. Growth in annuity as agreed 5% p.a. Outstanding corpus after paying 5th installment (out of 20) 8,691,667 Rs Number of years the corpus to last beginning 6th install Rs. NPER(1.065/1.05-1,475000*1.05, *1.065,0,1) Total installments including already 5 disbursed Increase in installments 6.36 installments Page 5

6 Section III Question 9 A retired couple has fixed pension of Rs. 30,000 p.m. while their current living expenses are at 31,000 p.m. They stay in their own house. You advise them to avail a loan under reverse mortgage which is an eligible lump sum of Rs. 40 lakh for 15 years at 12.5% p.a. interest. The annual interest is calculated after every 12 months on the pre-standing balance and added to the outstanding loan amount. You invest the available amount after withholding the excess normal expenses for the first year and considering 6% inflation thereafter at the beginning of every year. If the investment yield is 9% p.a., by what amount outstanding loan would exceed investment after 8 years? Post retirement income currently 30,000 Rs. p.m. Post retirement expenses currently 31,000 Rs. p.m. Loan eligible under reverse mortgage 4,000,000 Rs. Term of reverse mortgage 15 years Rate of interest 12.50% p.a. Loan outstanding at the end of 8 years 10,263,138 Rs *(1+12.5%)^8 Amount to be invested today 3,988,000 Rs *12 Rate of return expected from investment 9.00% p.a. Expected inflation 6.00% p.a. Amount under investment - end of year 1 4,346,920 Rs *(1+9%) Amount under investment - end of year 2 4,700,734 Rs. ( (31000*(1+6%)-30000)*12)*(1+9%) Amount under investment - end of year 3 5,060,603 Rs. ( (31000*(1+6%)^ )*12)*(1+9%) Amount under investment - end of year 4 5,425,524 Rs. ( (31000*(1+6%)^ )*12)*(1+9%) Amount under investment - end of year 5 5,794,312 Rs. ( (31000*(1+6%)^ )*12)*(1+9%) Amount under investment - end of year 6 6,165,576 Rs. ( (31000*(1+6%)^ )*12)*(1+9%) Amount under investment - end of year 7 6,537,697 Rs. ( (31000*(1+6%)^ )*12)*(1+9%) Amount under investment - end of year 8 6,908,798 Rs. ( (31000*(1+6%)^ )*12)*(1+9%) Difference between loan liability and investment (3,354,340) Rs Alternative method: Current annual expenses 372, *12 PV of 6% escalating expenses discounted at 9% for 8 years (2,704,570) PV(1.09/1.06-1,8,372000,0,1) PV of fixed pension discounted at 9% for 8 years (2,171,863) PV(9%,8,30000*12,0,1) PV of additional expenses recovered from RM loan disbursed 532, Balance loan amount to be invested for 8 years at 9% p.a. 3,467, Accumulated value after 8 years 6,908, *(1+9%)^8 Shortfall in value accumulated from loan liability (3,354,340) Section IV Question 6 A 40 year old male individual can get a 15-year with-profit life insurance policy of a company at an annual premium of Rs. 12,046 which gives a sum assured of Rs. 1.5 lakh. The company historically has declared reversionary bonuses and terminal bonus per thousand sum assured at Rs. 35 and Rs. 80, respectively. A term plan with same life and other parameters is generally available for an annual premium of Rs. 3,565. Find the return on investment component of the company s policy on surviving the term. Premium of with-profit policy 12,046 Rs. Premium of term policy 3,565 Rs. Excess premium on investment component 8,481 Rs. Terminal value on surviving the term 240,750 Rs. (150000/1000)*(35*15+80) Page 6 Return on investment component 7.63% p.a. RATE(15,-8481,0,240750,1)

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