Time Value of Money

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Nyenrode Business Universiteit Answers of study exercises Time Value of Money Time Value of Money Problem 1 Happy Harry has just bought a scratch lottery ticket and won €10,000. He wants to finance the future study of his newly born daughter and invests this money in a fund with a maturity of 18 years offering a promising yearly return of 6%. What is the amount available on the 18th birthday of his daughter? (1) (2) Calculate future value or present value or annuity ? Future value = PV * (1+ i)n Items: - PV i n = €10,000 = 6% = 18 years Answer: FV = €10,000 * 1.0618 = €10,000 * 2.854339 = €28,543.39 Problem 2 Rudy will retire in 20 years. This year he wants to fund an amount of €15,000 to become available in 20 years. How much does he have to deposit into a pension plan earning 7% annually? (1) Calculate future value or present value or annuity ? (2) Present value = FVn (1 + i) n Items: - FV i n = €15,000 = 7% = 20 years Answer: PV = €15,000 * (1/1.0720) = €15,000 * 0.258419 = €3,876.29 © Nyenrode Center for Finance - Dennis Vink 1 Nyenrode Business Universiteit Answers of study exercises Time Value of Money Problem 3 The National Savings Fund promises a monthly 0.75% return if you deposit €100 per month for 15 consecutive years. What amount will be accumulated after those 15 years? Calculate future value or present value or annuity? ⎡ (1 + i ) n − 1⎤ Future value = A * ⎢ ⎥ i ⎣ ⎦ (1) (2) Items: - Annuity -n -i = €100 = 15 years ???!!! = 0.75% p/m Answer: FVAN = €100 * (1.0075180 – 1) / 0.0075 = €100 * 378.40577 = €37,840.58 Problem 4 Willy has just bought a house. She estimates that the roof will have to be renewed at a cost of €25,000 after 20 years. To cover these costs, she intends to save an equal amount of money at the end of each

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