## Basic Calculations for Retirement Planning – CFP

Posted by Prashant Shah on January 4, 2017

- Interest Rate Calculation

Mathematics of Retirement Planning

Case

Current age of Mr. Shah is 30 years. His current household expenses are Rs.3,50,000 per annum. He estimates that post retirement he will need 80% of the pre-retirement expenses. Estimated inflation for his lifestyle is 6%. He wants to retire at the age of 60 years. He can invest money at 12% now and at 9% post retirement. His life expectancy is 80 years.

**Investment and Growing Annuity**

## Preeti Chhatwal said

Dear Prashant sir ,

Can you tell me how to solve this problem.

A buys second house at 60 lakh. Available loan is 40 lakh for 15 year at 9.5% rate. He liquidates his portfolio towards down payment stamp duty and furnishings. He has 5 lakh cash in hand at present. He is expected to save annually save 2 lakh. He would rent out new house at a rent of 25000 p.m. He will invest remaining cash in hand along with quarterly saving and rent received net of 20% maintenance charge on a quarterly basis beginning a quarter from now. Considering 8% p.a. growth in investment and real estate prices. What would be his net worth five years from now?

## jyoti mahant said

Hello Prashant sir,

I have recently given the retirement planning module a week back under the legacy program and I was not able to pass the exam. I was unable to solve the numerical and didn’t even get those which I prepared. I bought material from IMS Proschool, now I am completely blank about what to do and how to prepare, Kindly advise. The questions were really harder than those I practised.

## Abhinay said

Can some one please help me with the following question?

A Businessperson starts retirement planning with a lump sum annual investment of Rs. 3.50 lakh with an asset allocation between equity and bonds to 60:40. He increases this annual investment to 5% year on year. He has a target to accumulate a retirement fund of Rs. 3 crore and after 20 such annual investments. If the average annual returns from equity and bonds are considered respectively at 11% and 7%, what level of the target he might achieve.

a. The retirement fund target is expected to fall short by Rs. 46 lakh

b. The retirement fund target is expected to fall short by Rs. 23.25 lakh

c. The retirement fund target is expected to fall short by Rs. 23.50 lakh

d. The retirement fund target is likely to be achieved.

## Manish said

Dear Abhinay,

Here is the solution,

We have to find fv of growing annuity of equity and debt investments(begin mode).The formula of the same is

A*(1+R)*((1+R)^N-(1+G)^N)/(R-G).

A=ANNUAL INVESTMENTS

R=RETURN

N=NPER

G=GROWTH RATE

ANNUAL INVESTMENTS=350000

EQUITY=210000

DEBT=140000

FV OF EQUITY BY USING THE ABOVE FORMULA IS RS 16288356.

FV OF DEBT BY USING THE ABOVE FORMULA IS RS 9110736

TOTAL CORPUS ACHIEVED= RS 25399092

TOTAL CORPUS REQUIRED=RS 30000000

SHORTFALL= RS 4600907

## Prashant Shah said

Thanks Manish😊

## Manish said

Most Welcome Sir 🙂

## Abhinay said

Mr A has 10 more years of service left He had taken a Rs 30 lakh, 20-year 95% pa housing loan 5 years ago His investment account, which has an annual yield of 8.5%, has Rs 82 lakh. He contributes Rs 10,000 per month towards this investment. You advise him to fully repay the loan by his retirement by suitably directly part of his incremental investments to an increased EMI. What will be the value of his investment account on retirement?

190.07 lakh

208.13 lakh

191.56 lakh

209.71 lakh

## Abhinay` said

Hi Manish, thank you for your answer! Could you please also help me with the following questions:

A retired couple, of age 60 and 57, has a fair chance of either of them surviving until age 85. They shall invest retirement funds at 7.5% p.a. to sustain an inflation-adjusted annuity of Rs 4.5 lakh pa., average inflation estimated at 6%. To contain the risk of the longevity of each of them by 5 years, what additional funds would they require today to liquidate from their land investment, to be invested along with retirement fund?

a)19.43 lacs

b)16.31 lacs

c)12.40 lacs

d)14.76 lacs

You advise Xavier, of age 35 years, to start investing immediately for his retirement at age 60 years, with monthly contributions of Rs 10,000 The investment yield is 8.5% p.a. Your other client Maria, of age 25 years, can spare only Rs 5,000 per month towards retirement savings, If Maria wants to have the same retirement fund as Xavier’s when she completes 60 years of age, what differential refurn do you estimate for her investment than Xavier’s investment?

2.95% More

0.90% Less

4.05% less

4.40% more

## Manish said

Dear Abhinay,

1)

a)Find retirement corpus of couple by considering the life expectancy of 85.

Return:-7.50%

Inflation:-6%

Real Rate:-1.42%

nper:-28 yrs

pmt:- -450000

compute pv(begin mode)=10490097

b)Find retirement courpus of couple in case if there life expectancy increased by another 5 yrs to 90 yrs of age.

Nper:-33 yrs

pmt:- -450000

comput pv(begin mode)=11966450

Additional funds required right now to contain the risk of longevity:-11966450-10490097=1476353 rs

## Abhinay said

A childless couple, retired for 10 years, is surviving on a fixed monthly annuity of Rs 30.000 for life from the employer. The purchasing power of annuity has eroded in these ten years due to a constant 5% annual inflation. Their self-occupied house can be utilized for a reverse mortgage annuity, the assessed value of the house is Rs 80 lakh for a 15-year monthly annuity at 8.5% pa If they go for this reverse mortgage, what do you assess as the surplus income after meeting their present monthly expenses?

13575

22112

3250

15468

## Abhinay said

A childless couple, retired for 10 years, is surviving on a fixed monthly annuity of Rs 30,000 for life from the employer. The purchasing power of annuity has eroded in these ten years due to a constant 5% annual inflation. Their self-occupied house can be utilized for a reverse mortgage annuity, the assessed value of a house is Rs 80 lakh for a 15-year monthly annuity at 8.5% p.a. If they go for this reverse mortgage, what do you assess as the surplus income after meeting their present monthly expenses?

13575

22112

3250

15468

## Manish said

Dear Abhinay,

Their monthly expenses are not mentioned in question.Hence it is tough to calculate the surplus income.

## Abhinay said

Someone please please help me with the following problem:

A retired couple, of age 60 and 57, has a fair chance of either of them surviving until age 85. They shall invest retirement funds at 7.5% p.a. to sustain an inflation-adjusted annuity of Rs 4.5 lakh pa., average inflation estimated at 6%. To contain the risk of the longevity of each of them by 5 years, what additional funds would they require today to liquidate from their land investment, to be invested along with retirement fund?

a)19.43 lacs

b)16.31 lacs

c)12.40 lacs

d)14.76 lacs

## abinay said

Your client, who is 5 years from his retirement, looks forward to an annuity of Rs 10 lakh in the initial year of his retirement and wishes all subsequent annuities to retain the purchasing power for a retirement period of 35 years. The funds shall be invested to yield a real return of 2% p.a post- retirement. He has already accumulated Rs 1.5 crore. What monthly investments do you recommend until he retires at an expected return of 9% p.a.

64078

32140

64397

98089

## Manish said

Dear Abinay,

A)First we have to calculate the corpus required at retirement age by considering the annuity of Rs 10 lakh which will grow at 2% real rate every year for 35 yrs.

pmt= 1000000

Rate=2%

Nper=35 yrs

compute pv=? 25498591

B)Second calculate the monthly investments required to achieve this corpus by considering the already accumulated amt of Rs 1 crore 50 lakhs.

PV= -15000000

NOMINAL RATE=8.65%

NPER=5*12

FV=25498591

COMPUTE PMT=? 32140

## Abhinay said

Thanks a ton, Manish! This is very helpful. I have a couple of new questions that I have solved in excel. I was hoping if you can verify and cross-check my answers once. I can send you those questions on your email id. It will be a great help for me. I have already funked the 3 attempts and don’t want to repeat that again.

## Manish said

Dear Abhinay,

You can send here.It will be helpful for other students also,

## Abhinay said

You advise Xavier, of age 35 years, to start investing immediately for his retirement at age 60 years, with monthly contributions of Rs 10,000 The investment yield is 8.5% p.a. Your other client Maria, of age 25 years, can spare only Rs 5,000 per month towards retirement savings, If Maria wants to have the same retirement fund as Xavier’s when she completes 60 years of age, what differential refurn do you estimate for her investment than Xavier’s investment?

2.95% More

0.90% Less

4.05% less

4.40% more