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Sat 15 Oct, 2005 11:54 am
Q) Vernal Pool, wants to put aside a fixed fraction of her annual income as savings for retirement. Ms. Pool is now 40 years old and makes $40,000/yr. She expects her income to increase by 2% over inflation. (eg. 4% inflation means 6% increase in income). She wants to accumulate $500,000 in real terms to retire at age 70. What fraction of her income does she need to set aside? Assume her retirement funds are conservatively invested at an expected real rate of return of 5%/yr.
Can you help me with this question. I think i need to solve this using real cash flows and real interest rate. Income is growing at real rate of 2%, future value is 500000 in real terms. I can calculate the required amount (in real terms) to be saved each year under a growing annuity for 30 years with growth 2%, to accumulate this future value. Once i have that number i can compare it from the end of year salary.
Does this about right?
I just dont know where to plug in the values in the forumula and there are so many formulas which is confusing me! Please help!
Work out the present value of the 500000 that she wants at age 40. Then work out the present value of the income she has every year from 40 to 70[retirement].
The discount rate would normally be (1.05)^-1 for each year discounted back, but income and inflation rates add up to 1.04. So use a new rate of (1.05/1.04)-1 to discount the cashflows back to the present. Each amount would be X*whatever the discounted income is for each year. You add up all these incomes for 30 years, from 40 to 70, then solve for X which is the fraction needed for setting the income aside, X is the fixed percentage of income you need to set aside each year.
I hope you can understand my actuarial vision :p
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