Question

Determine m,n, and i for money earning 3.5% compounded quarterly for 123 months. m= (Type an integer or a decimal.) n= (Type an integer or a decimal.) i=% (Round to four decimal places as needed.)

Answer 1

To determine m, n, and i for money earning 3.5% compounded quarterly for 123 months, m equals 4 (since interest is compounded quarterly), n equals 41 (the number of quarterly periods in 123 months), and i equals 0.875% (the quarterly interest rate).

Step-by-step explanation:

The question aims to determine the values of m, n, and i for money earning a compound interest rate of 3.5% compounded quarterly over a period of 123 months.

The variable m represents the number of times interest is compounded per year, n represents the total number of compounding periods, and i is the interest rate per compounding period expressed as a percentage.

To find the values:

• m is the number of times the interest is compounded annually. Since it is compounded quarterly, m = 4.
• n is the total number of compounding periods. To calculate n, you multiply the number of years by m. Since there are 12 months in a year, 123 months is 123/12 = 10.25 years. n = 10.25 years * 4 = 41 (quarterly periods).
• Lastly, i is the annual interest rate divided by m. So, i = 3.5% / 4 = 0.875% per quarter, or as a decimal rounded to four places, i = 0.00875.

Therefore, the values are:

• m = 4
• n = 41
• i = 0.875% (or 0.00875 as a decimal)