You would like to have $50,000 saved at the end of Year 5. At the end of Year 2, you can deposit $7,500 for this purpose. If you earn 4.5 percent, how much must you deposit today to reach your goal assuming no other deposits are made

The amount that should be deposited today is $33254.58

Explanation:

The deposit should be such that the future value of the deposit made today and at the end of year 2 should be equal to $50000 after 5 years. Let the deposit made today be x. The equation for the future value will be,

50000 = x * (1+0.045)^5  +  7500 * (1+0.045)^3

50000 = x *  (1.045)^5  +  8558.745938

50000 - 8558.745938  =  x * (1.045)^5

41441.25406 / (1.045)^5  =  x

x = $33254.57769 rounded off to $33254.58

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