Chapter 6: Annuities

Question

Please assist with this question.

An investor deposits R2000 and then withdraws a fixed amount X at the end of every year starting one year after the deposit has been made. If, immediately after the 11th annual drawing, the investor has R400 left in the account, what fixed amount X must be withdrawn if interest is being calculated at a compound rate of 8% effective per annum?

Answer 1

X=R594.184387

Answer 2

2000 * 1.08^11 - X * {1-1.08^(-11)}/0.08 = 400

Therefore X = R594.184387

Comments

Not sure I understand...

You've FV'd the 2000 but then PV'd the annuity to time 11. Doesn't that imply the first annuity withdrawal is at time 12 (and the second at time 13 etc.), instead of at time 1?

Should it not be \(2000-x\times a_{\bar{11|}}=400V^{11}_{8\%}\)?

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Sorry, you’re right as well, I was supposed to have Sn instead of An.