Question

Which one of these formulas illustrates the compounding of interest?

a. 100 / (1+0.06)
b. 100 x (1+0.06)
c. 100 x (1+0.06) x (1+0.06)
d. 100 + 6 + 6 +6 +6

Answer 1

The formula that illustrates compound interest is '100 x (1+0.06) x (1+0.06)' as it represents the principal amount being compounded at a 6% interest rate over two periods.

Step-by-step explanation:

The formula that illustrates the compounding of interest among the given options is c. 100 x (1+0.06) x (1+0.06). This represents the calculation of interest on the principal amount of $100, compounded for two periods at a rate of 6%.

The formula for compound interest involves multiplying the principal by (1 + interest rate) raised to the power of the number of compounding periods. Here's a breakdown of how the formula applies:

• First period: $100 (principal) x (1+0.06) = $106 (new principal after one period)
• Second period: $106 (new principal) x (1+0.06) = $112.36 (future value after two periods)

For more compounding periods, you keep multiplying the new principal by (1 + interest rate). To find the total compound interest over a specific time period, you subtract the original principal from the future value after all compounding periods.

Answer 2

c. 100 x (1+0.06) x (1+0.06)

Step-by-step explanation:

c. 100 x (1+0.06) x (1+0.06)

Interest compounding takes the form of P*(1+r)^n,

where P is the principal, r is the interest rate, and n is the number of interest rate periods. If 6% interest is paid on $100 in principal once a year, the value at the end of the first year is $100*(1 + 0.060)^1. The second year would be:

$100*(1 + 0.060)^2 or $100*(1 + 0.060)*(1 + 0.060)