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 a. compounded semiannually

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 $A=P(1+r/n){}^{\mathrm{nt}}$, where n is the number of compounding periods per year.
3. Calculate the accumulated amount for each compounding frequency: semiannually (n=2), quarterly (n=4), and monthly (n=12) by substituting the respective n values into the formula.
4. For part d, use the continuous compounding formula $A=P{e}^{\mathrm{rt}}$, substituting the values of P, r, and t.
5. After substituting the values into the formulas, compute the expressions to find the accumulated amounts, then round each result to the nearest cent.

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 time in years. It accounts for interest earned on both the initial principal and accumulated interest.

Continuous Compounding Formula

Continuous compounding uses the formula A = Pe^(rt), where e is Euler's number (~2.718), to find the accumulated amount when interest is compounded an infinite number of times per year. This formula models the limit of compound interest as compounding frequency increases indefinitely.

Rounding and Financial Precision

Rounding to the nearest cent means expressing the final amount to two decimal places, reflecting typical currency format. This ensures practical financial accuracy and clarity when reporting investment values or interest calculations.