Chapter 25: Quick Study

QS B-1: Identifying Interest Rates in Tables (C1) To determine the future value using the future value of 1 table (Table B.2), adjust the interest rates and periods based on the compounding frequency: 1. 12% annual rate, compounded annually: o Use the 12% column and 2 periods row. 2. 6% annual rate, compounded semiannually: o Semiannual compounding means two periods per year at half the annual rate. o Use the 3% column (6% ÷ 2) and 4 periods row (2 years × 2). 3. 8% annual rate, compounded quarterly: o Quarterly compounding means four periods per year at a quarter of the annual rate. o Use the 2% column (8% ÷ 4) and 8 periods row (2 years × 4). 4. 12% annual rate, compounded monthly: o Monthly compounding results in twelve periods per year at 1/12th of the annual rate. o Use 1% per period (12% ÷ 12) and 24 periods row (2 years × 12). QS B-2: Interest Rate on an Investment (P1) Problem: Ken Francis invests $2,745 today to receive $10,000 after 15 years. Determine the annual interest rate. • • • Solution: Use the present value of 1 table (Table B.1) to identify the rate. Divide future value by present value to find the factor: 10,0002,745≈3.641. Look up 3.641 in the 15 periods row of Table B.1 to find the nearest interest rate, which should be around 8%. QS B-3: Number of Periods of an Investment (P1) Problem: Megan Brink invests $6,651 today at 6% annual interest, aiming to accumulate $10,000. Find the number of years required. • Solution: o Calculate the factor: 10,0006,651≈1.504 o Look up 1.504 in the 6% column of Table B.1 to find the closest match in terms of periods, which should be approximately 8 years. QS B-4: Present Value of an Amount (P1) Problem: Flaherty wants to invest for a return of $140,000 in five years at a 9% rate. Determine how much to pay today. • Solution: o Use the present value of 1 table (Table B.1) with i = 9% and n = 5. o PV factor at 9% for 5 years is approximately 0.6499. o Multiply: 140,000×0.6499=90,986 o Answer: Flaherty should be willing to pay $90,986 today. QS B-5: Future Value of an Amount (P2) Problem: CII, Inc. invests $630,000 at 12% annual interest for 10 years. Calculate the future value. • Solution: o Use the future value of 1 table (Table B.2) with i = 12% and n = 10. o FV factor at 12% for 10 years is approximately 3.1058. o Multiply: 630,000×3.1058=1,955,654 o Answer: The future value is $1,955,654. QS B-6: Present Value of an Annuity (P3) Problem: Beene Distributing will receive $150,000 annually for 6 years and requires a 7% return. Find the present value of this annuity. • Solution: o Use the present value of annuity table (Table B.3) with i = 7% and n = 6. o PV annuity factor at 7% for 6 years is approximately 4.7665. o Multiply: 150,000×4.7665=714,975 o Answer: Beene Distributing should pay $714,975 today. QS B-7: Future Value of an Annuity (P4) Problem: Claire Fitch invests $1,500 annually for 30 years at a 10% return. Determine the future value of this annuity. • Solution: o o o o Use the future value of annuity table (Table B.4) with i = 10% and n = 30. FV annuity factor at 10% for 30 years is approximately 164.4942. Multiply: 1,500×164.4942=246,741 Answer: The future value of the retirement fund is $246,741.30. Each calculation demonstrates how to use interest tables and the respective factors to find present or future values in financial scenarios. These concepts allow for efficient decision-making regarding investments, annuities, and other financial planning needs.