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...

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?

Asked on by elogical

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neela | High School Teacher | (Level 3) Valedictorian

Posted on

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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