Karen Smith is 25 years old, and intends to retire at age 65. According to the e
ID: 2774020 • Letter: K
Question
Karen Smith is 25 years old, and intends to retire at age 65. According to the estimation of life expectancy for Canadian women, she expects to live for 20 years in retirement. Therefore, Karen needs to save sufficient funds in the next 40 years to provide for herself for the subsequent 20 years. She plans to make monthly contributions to an equity-based mutual fund earning 10.5% annually. At retirement, Karen will put her savings into guaranteed investment certificates (GIC’s), paying 5.5%. Taking Canada Pension Plan income as well as inflation into account, Karen estimates that she will need a monthly income of $4000 throughout retirement. How much must she invest each month in mutual fund to ensure this standard of living? Assume that there is monthly compounding for the mutual fund.
Explanation / Answer
Total Retirement Corpus needed = 4000 * 12 * 20 = $960,000
Mutual Fund Annual Returns is 10.5%
Compounded monthly the interest e-rate will be (1+r/m)^m -1 where r =10.5-0.1050 and m =12 (monthly compounding)
Therefore Effective interest rate is (1+0.1050/12)^12-1 = 11.02%
Now to find out the monthly investment, we use the excel formula pmt(rate, nper, pv, [fv])
Where rate =11.2% or 0.1102, nper = 40 years, pv =0, fv=-960,000
Hence pmt(0.1102,40,0,-960,000) = 1,437.45
Hence a monthly Investment of $1,437.45 is needed to be invested
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