Question

Suppose $100 is invested in an account yielding interest at a nominal rate of 4% per year. Find the balance three years later if the interest is compounded monthly, quarterly, annually

Answer 1

For monthly compounding, the balance is $112.68.

For quarterly compounding, the balance is $112.55.

For annual compounding, the balance is $112.48.

Step-by-step explanation:

To find the balance three years later, we need to calculate the compound interest using the given nominal rate.

For monthly compounding, we use the formula:

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

Where:

• A is the final amount
• P is the principal amount (initial investment)
• r is the annual nominal interest rate (expressed as a decimal)
• n is the number of times interest is compounded per year
• t is the number of years

Substituting the values into the formula, we have:

A = $100(1 + 0.04/12)^(12×3)

= $112.68 (rounded to 2 decimal places).

For quarterly compounding, we use the same formula but change the value of n to 4:

A = $100(1 + 0.04/4)^(4×3)

= $112.55 (rounded to 2 decimal places).

Finally, for annual compounding, we use the formula:

A = $100(1 + 0.04)^3

= $112.48.