02%20time%20value%20of%20money%20part%201%20-%20lecture%20problems%20solutions

# 02%20time%20value%20of%20money%20part%201%20-%20lecture%20problems%20solutions

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Solutions to lecture problems – time value of money part 1 If Eric invests \$500 today in an account that earns 8% per year in simple interest, how much will he have in 15 years? With simple interest, C 0 today grows to the following in t periods: C 0 × (1 + (simple interest rate per period × t)) So, Eric would have 500 × (1 + (.08 × 15)) = 500 × (1 + 1.2) = \$1,100 Eric would earn \$600 in interest as .08 × 500 = \$40 per year for 15 years, so he would have \$500 + \$600 = \$1,100 in 15 years 1

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Solutions to lecture problems – time value of money part 1 If Jane can earn 7% per year in compound interest, how much would Jane need to invest today to have as much as Eric in 15 years? We know from the previous problem that Eric will have \$1,100 in 15 years With compound interest, FV t = C 0 × (1 + r) t FV t = \$1,100 = the amount that Jane wants in 15 years r = .07 = the compound interest rate t = 15 = the number of years in the future from the reference period (today) that Jane wants to have \$1,100 C 0 = amount invested today = ? FV t = C 0 × (1 + r) t 1,100 = C 0 × (1.07) 15 So C 0 = 1,100 / (1.07) 15 = 398.69 Jane would need to invest \$398.69 today at 7% per year in compound interest to have \$1,100 in 15 years Confirm FV t = C 0 × (1 + r) t = 398.69 × (1.07) 15 \$1,100 2
Solutions to lecture problems – time value of money part 1 If Martha invests \$500 today in an account that earns 9% per year in compound interest, how much will she have in 12 years? With compound interest, FV t = C 0 × (1 + r) t In this case: C 0 = 500 r = .09 t = 12 FV 12 = 500 × (1.09) 12 = \$1,406.33 Martha would have \$1,406.33 in 12 years 3

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Solutions to lecture problems – time value of money part 1 If Carl can invest \$600 today, then how much would Carl need to earn each year as a simple interest rate to have as much as Martha in 12 years? We know from the previous problem that Martha will have \$1,406.33 in 12 years With simple interest, C 0 today grows to the following in t periods: C 0 × (1 + (simple interest rate per period × t)) C 0 = amount invested today = 600 t = 12 = the number of years in the future from the reference period (today) that Carl wants to have \$1,406.33 1,406.33 = C 0 × (1 + (simple interest rate per period × t)) 1,406.33 = C 0 + (C 0 × simple interest rate per period × t) 1,406.33 = 600 + (600 × simple interest rate per period × 12) So 1,406.33 – 600 = 806.33 = (600 × simple interest rate per period × 12) So 806.33 / (600 × 12) = simple interest rate per period = 806.33 / 7200 = .11199 ≈ .1120 Carl would need to earn a simple interest rate per year of 11.20% on his investment of \$600 today to have \$1,406.33 in 12 years Confirm With simple interest, C 0 today grows to the following in t periods: C 0 × (1 + (simple interest rate per period × t)) = 600 × (1 + (.112 × 12)) = 600 × (1 + 1.344) = 600 × 2.344 = \$1,406.40 ≈ \$1,406.33 4
Solutions to lecture problems – time value of money part 1 Suppose you expect to receive a gold medallion in 2 years when you graduate that will be

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## This note was uploaded on 02/03/2011 for the course FINANCE 301 taught by Professor Murray during the Spring '09 term at George Mason.

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02%20time%20value%20of%20money%20part%201%20-%20lecture%20problems%20solutions

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