Use the compound interest formulas A = P (1+ r/n)^nt and A =Pe^rt to solve exercises 53-56. Round answers to the nearest cent. Find the accumulated value of an investment of \$10,000 for 5 years at an interest rate of 1.32% if the money is c. compounded monthly.

Verified step by step guidance

1. Identify the given values: principal P = 10,000, time t = 5 years, interest rate r = 1.32% (which should be converted to decimal form as 0.0132).
2. For parts a, b, and c, use the compound interest formula $A=P(1+r/n){\left(}^n$, where n is the number of compounding periods per year.
3. Calculate the accumulated value for each compounding frequency: semiannually (n=2), quarterly (n=4), and monthly (n=12) by substituting the values of P, r, n, and t into the formula.
4. For part d, use the continuous compounding formula $A=P{e}^{^}$, substituting the values of P, r, and t.
5. After substituting the values into the respective formulas, calculate the expressions and round the results to the nearest cent to find the accumulated values.

Key Concepts

Compound Interest Formula

The compound interest formula A = P(1 + r/n)^(nt) calculates the accumulated amount A after t years, where P is the principal, r is the annual interest rate, n is the number of compounding periods per year, and t is the time in years. It accounts for interest earned on both the initial principal and the accumulated interest.

Continuous Compounding Formula

The continuous compounding formula A = Pe^(rt) models interest compounded an infinite number of times per year, where e is Euler's number (~2.71828). This formula gives the maximum possible accumulated value for a given principal, rate, and time, reflecting continuous growth.

Rounding and Financial Precision

Rounding to the nearest cent means expressing the final amount to two decimal places, reflecting standard currency format. This ensures practical and accurate financial reporting, as monetary values are typically handled in dollars and cents.