You need to accumulate $10,000. to do so, you plan to make deposits of $1,250 per year, with the first payment being made a year from today, in a bank account that pays 12 percent interest, compounded annually. your last deposit will be less than $1,250 if less is needed to round out to $10,000. how many years will it take you to reach your $10,000 goal, and how large will the last deposit be?

It take you 6 years.  The Last deposit will be  34,58

Explanation:

To get how many years will take to accumulate $10000.  First we have to capitalize the different deposits.  

For example,  

First deposit will be  $1,250

At the end of this year we will have $1,400. We use formula of interest

A=P (1+r)ⁿ

A=Final amount  

P= Principal ( deposit)  

r= interest rate

n= time

A=1250 (1+0,12)¹=1400

Year 2,  we will deposit $1,250 and we have accumulated $1,400

So,  P will be $1250 + $1400=$2650

A=2650 (1+0,12)¹=$2.968

Year3  = deposit 1250+ accumulated 2.968

A=4.724,16

Year4  = deposit 1250+ accumulated4.724,16

A=6.691,06

Year5  = deposit 1250+ accumulated6.691,06

A=8.893,99

We are close to our goal so now we have to do another calculus

Year6  = A Final = 10000= (deposit +accumulated) * 1,12

Our unknown here is the deposit

So,  deposit=(10000/1,12)-8.893,99

Last deposit= 34,58

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