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

Year 3 = deposit 1250 + accumulated 2.968

A = 4.724,16

Year 4 = deposit 1250 + accumulated 4.724,16

A = 6.691,06

Year 5 = deposit 1250 + accumulated 6.691,06

A = 8.893,99

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

Year 6 = 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