Many IRA fund managers argue that investors should invest at the beginning of the year rather...

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Many IRA fund managers argue that investors should invest at the beginning of the year rather than at the end. What is the difference to an investor who invests $2,000 per year at 11 percent over a 30 year period? Excel hint: Type 0; ordinary annuity Type- 1: annuity due

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Answer 1

Answer #1

Type = 0 - ordinary annuity, payments are made at end of each period

FV = P[(1+r)ⁿ -1]/r

where, P = 2000
r = 11% = 0.11
n = 30

=> FV = 2000(1.11³⁰ - 1] /0.11 = $398,041.76

Type = 1 - annuity due, payments are made at starting of each period

FV = P [((1 + r)ⁿ - 1) / r])(1 + r)

where, P = 2000
r = 11% = 0.11
n = 30

=> FV = 2000((1.11)³⁰ - 1) / 0.11)(1.11) = $441,826.35

Hence, difference between annuity due and ordinary annuity = 441826.35 - 398041.76 = $43,784.59

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Answer 2

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