Nicole Clark wants to retire in 15 years. She estimates she will need $43,700 pe

Question

Nicole Clark wants to retire in 15 years. She estimates she will need $43,700 per year during her retirement and she guesses her retirement will last 21 years. She can invest at 5.22% per annum and she pays no tax. Assume all transactions occur at the end of each year so her final payment into the fund is the day before she retires and her first withdrawal is a year after that. 1. (a) How much money must Nicole have accumulated in her retirement fund on the day she retires? (b) How much money must she save each year to achieve her goal?

Explanation / Answer

a. Amount of money Nicole must have accumulated in her retirement fund on the day she retires is the PV at yr. 15 end/yr.16 beginning of 21 nos. year-end (yr.16 end to yr.36 end) withdrawals of $ 43700 at 5.22% so, using the PV of ordinary annuity formula, PV=Pmt.*(1-(1+r)^-n)/r & substituting the above values, PV=43700*(1-(1+0.0522)^-21)/0.0522 549593 Nicole must have accumulated ,on the day of retrement(including the 15th deposit)=$ 549593 b. She needs to save "x" amt. each year-end (yr.1 end to yr. 14 end) at 5.22% p.a. so that its Future value at yr.15 end is (549593-x) so, using the FV of ordinary annuity formula, FV=Pmt.*((1+r)^n-1)/r & substituting the above values, (549593-x)=x*(1.0522^14-1)/0.0522 26295.7 or 26296 So, amt. she must save each yr. end = $ 26296

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