Find The Amount That $800 Principal Will Accumulate

Question

Find the amount that a principal of 800 will accumu Find the amount that a principal of $800 will accumulate in 12 years for each given account: a. 7% simple interest b. 7% compounded quarterly c. 7% compounded monthly

Dr. Jack HW Helper · Accepted Answer

Calculating the future value of an investment involves understanding the type of interest applied—simple or compound—and applying the correct formula accordingly. Given an initial principal of $800 over a period of 12 years at an annual interest rate of 7%, we can determine the accumulated amount under each interest scheme. a. Simple Interest Simple interest is straightforward, calculated as a percentage of the initial principal and does not compound over time. The formula is: Future Value (FV) = Principal (P) × (1 + r × t) Where: P = 800 r = 0.07 (7% expressed as a decimal) t = 12 years Substituting the values: FV = 800 × (1 + 0.07 × 12) = 800 × (1 + 0.84) = 800 × 1.84 = 1472 Thus, with simple interest, the account will grow to a total of $1,472 after 12 years. b. Compound Interest (Quarterly) Compound interest considers the interest earned in each period to be added to the principal, which then earns interest in subsequent periods. The formula is: FV = P × (1 + r/n)^(n×t) Where: P = 800 r = 0.07 n = 4 (quarterly compounding) t = 12 Substituting the values: FV = 800 × (1 + 0.07/4)^(4×12) = 800 × (1 + 0.0175)^{48} = 800 × (1.0175)^{48} Calculating (1.0175)^{48}: (1.0175)^{48} ≈ e^{48 × ln(1.0175)} ≈ e^{48 × 0.0173} ≈ e^{0.8304} ≈ 2.294 Therefore: FV ≈ 800 × 2.294 ≈ 1835.20 With quarterly compounding, the amount after 12 years would be approximately $1,835.20. c. Compound Interest (Monthly) Using the similar formula but with monthly compounding: FV = P × (1 + r/n)^(n×t) Where: P = 800 r = 0.07 n = 12 (monthly compounding) t = 12 Substituting: FV = 800 × (1 + 0.07/12)^{12×12} = 800 × (1 + 0.0058333)^{144} = 800 × (1.0058333)^{144} Calculating (1.0058333)^{144}: ~ e^{144 × ln(1.0058333)} ≈ e^{144 × 0.005817} ≈ e^{0.837} ≈ 2.310 Therefore: FV ≈ 800 × 2.310 ≈ 1848.00 With monthly compounding, the accumulated amount in 12 years will be approximately $1,848.00. Conclusion In summary, for a principal of $800 invested over 12 years at 7%, simple interest yields about $1,472;

Find The Amount That $800 Principal Will Accumulate ✓ Solved

Find the amount that a principal of 800 will accumu

Sample Paper For Above instruction

a. Simple Interest

b. Compound Interest (Quarterly)

c. Compound Interest (Monthly)

Conclusion

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