Compound Interest Question.

Max is planning to take three years off work to travel the world. He plans to start this holiday in 5 years time and is looking to invest money now so that he can receive an annual annuity payment of $15,000 for each of the 3 years he is not working. How much he invest now to secure such payments, given that the interest rate is 8.3% p.a. compounded annually?

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**CHICKEN**

Let Max invest P.

Then P in 5years with compound interest becomes = (1.083^5)P .

After that he should recieve $ 35000 for the first year of his travel. Then the balance = $ {(1.085^5)P -35000}.

For the next year the above balance, (1.083^5)P - 35000 becomes with interest = [(1.083^5P- 35000]1.083 and Max Recieves $35000 for the 2nd year of the travel.

Now the balance is $ [(1.083)^5*P -35000](1.083)-35000. And this balance earns interest and along with interest it becomes {[(1.083^5 P - 3500)1.083 -35000] 1.83 } and he recieves another $35000 and at this point his balance should be zero .

Therefore 1.083^7*P - 350001.083^2-35000*1.083 -35000 = 0.

Or P = 35000 (1.083^2+1.083+1) = 35000*3.255889

Therefore P = 3500*3.255889/(1.083^7) = 65214 dollars.

**Therefore he should invest $65214 sothat recieves $35000 each of the 3 years and at the end the balance is zero.**

Tally : $ 65214 becomes with 8.3% compound interest in 5 years = 65214*1.083^5 = $97159.

After recieving $35000, the balance is $(97159-35000) = $62159.

$(62159) becomes with 8.3% compound interest for 1 year = $62159*1.083 = $67 318.

After recieving $35000 , the balance to earn interest in 2nd year is $(67318 -35000) = $32318.

$ 32318 should becomes along with interest at the end of the 2nd year $(3218)*(1.083) = $35000.

So Max takes $35000 for the 3rd year travel and now the balnce is zero.

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