# Financial Math Review

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FIN 203 QUESTIONS AND ANSWERS 1. You plan to deposit \$2,000 in a bank today that will pay 6% annually. Question 1a What is the future value of this sum at the end of 10 years? What is the future value at the end of 10 years if the bank pays 6% compounded quarterly? If it is compounded continuosly? Explain the results. Annual: PV = -2000, I/YR = 6; N = 10; solve for FV = \$3581.70 Quarterly: I/YR = 6/4 = 1.5; N = 10*4 = 40; solve for FV = \$3628.04 Continuously: -2000*(e**.06**10) = \$3,644.24 FV increases with the number of compounding periods Question 1b What will be the total accumulated amount at the end of 10 years if in addition to the initial \$2,000, you also deposit \$4,000 in year 4 and \$8,000 in year 8? Assume an annual 6% interest rate for all ten years. First cash flow: FV = 3581.70 (already done) Second cash flow: PV = -4000, N = 6, I/YR = 6, solve for FV = 5674.08 Third cash flow: PV = -8000, N=2, I/YR = 6; solve for FV = 8988.80 ANSWER: 3581.70+5674.08+8988.80 = \$18,244.58 Question 1c Using the information from Question 1b, what will be the total accumulated value at the end of 10 years, if the interest rate is expected to be 6% for only the first three years, followed by 8% for the next five years, and 10% thereafter? First cash flow: PV = -2000, N=3, I/YR =6, solve for FV = 2382.03 PV = -2382.03, N = 5, I/YR = 8, solve for FV = 3499.98 PV = -3499.98, N = 2, I/YR = 10, solve for FV = 4,234.97 Second cash flow: PV = -4000, N = 4, I/YR = 8, solve for FV = 5441.96 PV = -5441.96, N = 2, I/YR = 10, solve for FV = 6584.77 Third cash flow: PV = -8000, N = 2, I/YR = 10, solve for FV = 9680.00 ANSWER: 4234.97 + 6584.77 + 9680.00 = \$20,499.74 Question 1d Using the information from 1b, what equal amounts should be withdrawn in years 5 an 6, if the total accumulated value at the end of ten years is