Question

The basic compound interest formula has 5 variables

• A = the total amount in the account
• P= the principal or initial amount invested
• r = the annual interest rate
k = the number of times the interest is compounded in 1 year
• t = time, in years
tk
A = P(1 + )"
Use the formula to find the compound interest earned, if the investment amount (P) is $10,000, the rate (r) is 3%, and the investment i
compounded monthly for 1 year.
Select one:
O a. $304.16
O b. $25
O c. $10,304.16
O d. $10,025

Answer 1

Using the compound interest formula, the correct answer for the compound interest earned on a $10,000 investment, at a 3% annual interest rate compounded monthly for 1 year, is $304.16.

Step-by-step explanation:

To calculate the compound interest earned on an investment amount (P) of $10,000, with an annual interest rate (r) of 3%, compounded monthly for 1 year, we will use the compound interest formula:

A = P(1 + r/k)kt

Where: A = the total amount in the account after interest P = the principal or initial amount invested ($10,000) r = the annual interest rate (0.03) k = the number of times interest is compounded per year (12) t = time in years (1)

Placing the values into the formula gives us:

A = $10,000(1 + 0.03/12)12(1)

A = $10,000(1 + 0.0025)12

A = $10,000(1.0025)12

A = $10,000(1.03042)

A = $10,304.16

The total future amount after 1 year is $10,304.16. The compound interest earned is the difference between the future value and the present value of the principal:

Compound interest = A - P

Compound interest = $10,304.16 - $10,000

Compound interest = $304.16

Therefore, the correct answer is a. $304.16.