Question

An annuity that pays out payments that increase by 0.75% each payment period will be paid out over a 10 year period will be purchased with interest of 6% compounded monthly. If the payments will start at $1000 the first month, how much will need to be in the account to sustain the 10 years of payments?

Answer 1

Calculating the amount needed to sustain the paymenst for 10 years:-

$Present Value of Growing Annuity = C*\frac{1-[(1+g)^{n}*(1+r)^{-n}]}{r-g}$

Where, C= First Payment= $1000

r = Periodic Interest rate = 6%/12 =0.5%

g = Growth rate of further payments = 0.75%

n= no of periods = 10years*12 = 120

$Present Value = 1000*\frac{1-[(1+0.0075)^{120}*(1+0.005)^{-120}]}{(0.005-0.0075)}$

$Present Value = 1000*\frac{1-[2.45135707812*0.54963273336]}{(-0.0025)}$

Present Value = $138,938.44

So, will need to be in the account to sustain the 10 years of payments is $138,938.44

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