Question 1179081
Let's break this problem into two parts:

**Part 1: Calculate the Accumulated Value of Nick's Savings Account**

1.  **Deposits:** $190 every three months (quarterly)
2.  **Time Period:** 3 years
3.  **Interest Rate:** 3% convertible quarterly (0.03/4 = 0.0075 per quarter)
4.  **Number of Deposits:** 3 years * 4 quarters/year = 12 deposits

We can use the future value of an ordinary annuity formula:

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

Where:

* FV = Future Value
* P = Periodic Payment ($190)
* r = Interest Rate per Period (0.0075)
* n = Number of Periods (12)

FV = 190 * [((1 + 0.0075)^12 - 1) / 0.0075]
FV = 190 * [(1.0075^12 - 1) / 0.0075]
FV = 190 * [(1.093806897 - 1) / 0.0075]
FV = 190 * [0.093806897 / 0.0075]
FV = 190 * 12.50758627
FV ≈ $2376.44

**Part 2: Calculate Nick's Monthly Car Loan Payment**

1.  **Car Price:** $14,000
2.  **Down Payment:** $2376.44 (from the savings account)
3.  **Loan Amount:** $14,000 - $2376.44 = $11,623.56
4.  **Loan Term:** 4 years
5.  **Interest Rate:** 3% convertible semiannually (0.03/2 = 0.015 per 6 months)
6.  **Number of Semiannual Periods:** 4 years * 2 = 8
7.  **Number of Monthly Payments:** 4 years * 12 months/year = 48

First, we need to find the equivalent monthly interest rate.

* (1 + 0.015)^2 = 1.030225. This is the effective annual rate.
* (1.030225)^(1/12) = 1.002470126. This is the monthly multiplier.
* Monthly Interest Rate = 1.002470126 - 1 = 0.002470126

Now, we can use the loan payment formula:

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

Where:

* M = Monthly Payment
* P = Loan Amount ($11,623.56)
* r = Monthly Interest Rate (0.002470126)
* n = Number of Monthly Payments (48)

M = 11623.56 * [0.002470126 * (1.002470126)^48] / [(1.002470126)^48 - 1]
M = 11623.56 * [0.002470126 * 1.127493457] / [1.127493457 - 1]
M = 11623.56 * [0.002785721] / [0.127493457]
M = 11623.56 * 0.021850327
M ≈ $253.97

**Answer:**

Nick's monthly car loan payment will be approximately $253.97.