You plan to purchase a motorcycle in four years and intend to save $3,500 annually, starting immediately. You will make four deposits into an account with a 5.7% interest rate. Based on these conditions, how much will you have in four years? a. $16,112 b. $16,918 c. $17,763 d. $18,652 e. $19,584

To calculate how much you will have in four years after saving $3,500 annually, we can use the future value of an annuity formula for an investment which compounds annually. The formula for the future value of an annuity is:

FV = P * [(1 + r)^n - 1] / r

FV = future value of the annuity, P = annual payment (or deposit), r = annual interest rate (as a decimal), n = number of payments.

Here, P is $3,500, r is 5.7% (or 0.057 as a decimal) and n is 4 (since you are making four annual deposits). 

Plugging these values into the formula, we get:

FV = $3,500 * [(1 + 0.057)^4 - 1] / 0.057

Now, let's calculate this step-by-step:

1. Calculate the growth factor for each year: 

(1 + 0.057) = 1.057 2. Raise this factor to the power of n (4 years): (1.057)^4 3. 

Calculate the future value factor using the previous result: 

[(1.057)^4 - 1] 

= (1.2467 - 1) 

= 0.2467 (rounded to four decimal places for simplicity) 

4. Divide this factor by r (0.057):

 0.2467 / 0.057 

= 4.3298 (rounded to four decimal places) 

5. Multiply this result by the annual payment of $3,500: 

$3,500 * 4.3298 

= $15,154.30

This is the future value of the annuity portion of the calculation. However, we must also add the final year's deposit since it does not earn any interest (as it's deposited at the end of the period).

Thus, the total amount you'd have after the four years is,

$15,154.30 (interest earned) + $3,500 (final year's deposit)

 = $18,654.30

 (rounded to the nearest dollar, since we approximated during our calculations).

None of the options you provided exactly match this result, so either there's a rounding issue in our calculation, or the options given might have a mistake. However, option d. $18,652 is the closest to our calculated amount, and it's likely meant to be the correct answer, given the slight differences could be due to the rounding differences in intermediate steps.