Question

Use the compound interest formula: Determine the value of $5,000 invested at 3.6% annual interest compounded as follows: give as money (dollars & amp, cents)

a) Monthly for 12 years.
b) Quarterly for 12 years.
c) Daily for 12 years.

Answer 1

The compound interest for a $5,000 investment at 3.6% annual interest compounded monthly, quarterly, and daily over 12 years can be calculated using the compound interest formula. Using the formula, the amounts for each compounding frequency will show the power of compound interest over time, especially with larger sums and longer periods.

Step-by-step explanation:

To determine the value of $5,000 invested at 3.6% annual interest compounded for different periods over 12 years, we will use the compound interest formula:

A =
`P(1 + r/n)^(nt)`

Where:

• A = the future value of the investment/loan, including interest
• P = the principal investment amount ($5,000)
• r = the annual interest rate (decimal) (3.6% or 0.036)
• n = the number of times that interest is compounded per year
• t = the time the money is invested for in years (12 years)

For monthly compounding (n=12), we have:

A =
`$5,000(1 + 0.036/12)^((12*12))`

For quarterly compounding (n=4), we have:

A =
`$5,000(1 + 0.036/4)^((4*12))`

For daily compounding (n=365), assuming 365 days in a year, we have:

A =
`$5,000(1 + 0.036/365)^((365*12))`

Using these calculations, you will find the total amount of money after 12 years including compound interest for each compounding frequency. Keep in mind that as shown in Step 8 of the provided information, compound interest can greatly increase the total amount of money over time compared to simple interest, especially with larger sums of money and over longer periods of time.