Question

Describe the effect an increase in i, the interest rate applied to the present value, has on the monthly payment P in the formula P = P V times StartFraction i over 1 minus (1 i) superscript negative n Baseline EndFraction a. An increase in i, the interest rate, will not change P, the monthly payment. B. An increase in i, the interest rate, will create an increase in P, the monthly payment. C. An increase in i, the interest rate, will create a decrease in P, the monthly payment. D. An increase in i, the interest rate, can increase or decrease P, the monthly payment, depending on the value of PV.

Answer 1

The A option is correct.

Ratio and proportion

A ratio is an ordered pair of numbers a and b, written as a/b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other.

Given

The interest rate applied to the present value has on the monthly payment P in the formula

$\rm P = PV(\dfrac{i}{1-i})^{-n}$

To find

The effect an increase in i.

How to find it?

$\rm P = PV(\dfrac{i}{1-i})^{-n}$

on simplifying the equation, we get

$\rm P = PV(\dfrac{i}{1-i})^{-n}\\\\P = PV\dfrac{1}{(\frac{i}{1-i})^n}\\\\\\P = PV(\dfrac{1-i}{i})^{n}\\\\P = PV(\dfrac{1}{i} - 1)^{n}$

Let n be the constant, then the equation will be

$\rm P = PV(\dfrac{1}{i} - 1)^{n}\\\\\dfrac{1}{V} \propto \dfrac{1}{i}\\\\V \propto i$

It is clear that V is proportional to i.

An increase in i, the interest rate, will not change P, the monthly payment.

Thus, the A option is correct.

More about the ratio and the proportion link is given below.

brainly.com/question/165414