The Formula for Finding the Monthly Payment for an Amortized $M = P \left[ \frac { R } { 1 - ( 1 + R ) ^ { - N } } \right]$

question 4

Short Answer

The formula for finding the monthly payment for an amortized loan is: $M = P \left[ \frac { R } { 1 - ( 1 + R ) ^ { - N } } \right]$ , where $M$ is the monthly payment, $R$ is the interest rate PER MONTH, and $\mathrm { N }$ is the number of months. Find the monthly payment on a car loan of $\$ 20,000$ at $12 \%$ for 5 years.

---

Definitions:

Partial Sum

The sum of a specified number of terms at the beginning of a sequence.

Rebounds

In sports, the act of successfully retrieving the ball after a missed shot.

Geometric Sequence

A numerical series where each number after the first is determined by multiplying the prior number by an unchanging, non-zero numerical value, denoted as the common ratio.

Partial Sum

A partial sum is the sum of the first n terms of a sequence, often used in the context of series to understand the progression or to investigate convergence.