Question

# You want to have \$300,000 in real terms 7 years from now. You expect inflation over...

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?

 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

#### Earn Coins

Coins can be redeemed for fabulous gifts.