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In calculating the monthly payment for a loan with an [tex]$8.5 \%$[/tex] interest rate compounded monthly, what value should be used for [tex]$i$[/tex], the interest rate per period, as it appears in the following formula?
[tex]\[ P = PV \cdot \frac{i}{1 - (1 + i)^{-n}} \][/tex]

A. 8.5
B. 0.71
C. 0.085
D. 0.0071

Please select the best answer from the choices provided:

A
B
C
D


Sagot :

To determine the interest rate per period (monthly interest rate) given an annual interest rate compounded monthly, follow these steps:

1. Identify the annual interest rate:
- The annual interest rate given is [tex]\(8.5\)[/tex]%.

2. Convert the annual interest rate to a decimal:
- Since percentage means per hundred, convert the annual interest rate from percentage to decimal form by dividing by [tex]\(100\)[/tex]:
[tex]\[ 8.5\% = \frac{8.5}{100} = 0.085 \][/tex]

3. Convert the annual rate to a monthly rate:
- To get the monthly interest rate from the annual rate, divide by the number of months in a year (12):
[tex]\[ \text{Monthly Interest Rate} = \frac{0.085}{12} \][/tex]

4. Perform the division:
- When you divide [tex]\(0.085\)[/tex] by [tex]\(12\)[/tex], you get:
[tex]\[ \frac{0.085}{12} \approx 0.007083333333333334 \][/tex]

Therefore, the value that should be used for [tex]\(i\)[/tex] in the formula is approximately [tex]\(0.0071\)[/tex].

So, from the choices provided:

a. 8.5
b. 0.71
c. 0.085
d. 0.0071

The best answer is:

D.