You want to save an amount today that will pay for your futureannual food bills...

You want to save an amount today that will pay for your future annual food bills that will start next year, and go for 20 years. The current annual cost of your food bill is $6,155, but the cost is rising at 3% per year. How much would you have to invest today, to fully pay for your future annual food bills if your investments earn 6.81% APR nominal (annual compounding).

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Expert Solution

- Current Annual cost of Food = $6155

You wanted to save enough today such that will pay for your future annual food bills. The annual food payment will start next year.

The First payment towards food cost which start next year = Current Cost*(1+ cost of Rising)

= $6155*(1+0.03)

= $6339.65

Now, Calculating the Present value of annual food cost that start next year using Present value of Growing annuity formula:-

Where, C= First Payment = $6339.65

r = Periodic Interest rate = 6.81%

g = Annual rising rate = 3%

n= no of periods = 20

Present Value = $85,922.70

So, the amount you need to invest today is $85,922.70

jeff jeffy answered 2 years ago

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