Question

You want to have $300,000 in real terms 7 years from now.

You expect inflation over that time period to be 4% per year. Your
investments earn 7% APR (nominal) compounded annually.

Based on your expectations, you construct a growing nominal annuity
to meet your investment target. What is the nominal cash-flow you
would have to deposit in year 5 if inflation turns out to what you
expected?

Answer #1

The growing annuity would be | |||

FV[GA] = P*[((1+r)^n-(1+g)^n))/(r-g) | |||

where | |||

P = The first payment | |||

r = rate per periiod | |||

g = growth rate (here inflation) | |||

n = number of periods | |||

The amount required in nominal terms = 300000*1.04^7 = | $ 394,780 | ||

Substituting values we have | |||

394780 = P*[1.07^7-1.04^7)/(0.07-0.04)] | |||

Solving for P | |||

P = 394780/((1.07^7-1.04^7)/0.03)) | $ 40,860.49 | ||

So the first payment = $40860.49 | |||

The fifth payment would be 40860.49*1.04^4 = | $ 47,800.99 | ||

Check: | |||

Year | Payment with 4% increase every year | FVIF at 7% | FV |

1 | 40860.49 | 1.50073 | 61321 |

2 | 42494.91 | 1.40255 | 59601 |

3 | 44194.71 | 1.31080 | 57930 |

4 | 45962.49 | 1.22504 | 56306 |

5 | 47800.99 | 1.14490 | 54727 |

6 | 49713.03 | 1.07000 | 53193 |

7 | 51701.56 | 1.00000 | 51702 |

Total amount | 394780 |

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