Question

5A-1

FV CONTINUOUS COMPOUNDING If you receive $15,000 today and can invest it at a 6% annual rate compounded continuously, what will be your ending value after 15 years?

5A-2

PV CONTINUOUS COMPOUNDING In 7 years, you are scheduled to receive money from a trust established for you by your grandparents. When the trust matures there will be $200,000 in the account. If the account earns 9% compounded continuously, how much is in the account today?

5A-3

FV CONTINUOUS COMPOUNDING Bank A offers a nominal annual interest rate of 7% compounded daily while Bank B offers continuous compounding at a 6.9% nominal annual rate. If you deposit $1,000 with each bank, what will be the difference in the two bank account balances after two years?

5A-4

CONTINUOUS COMPOUNDED INTEREST RATE In order to purchase your first home 6 years from today, you need a down payment of $40,000. You currently have $20,000 to invest. To achieve your goal, what nominal interest rate, compounded continuously, must you earn on this investment?

Answer 1

For continuous compounding, the formula is:

FV = PV * e^rt

QUESTION 5A -1

PV = 15000, r = 6%, t = 15

FV = 15000 * e^{(6% * 15)}

FV = 15000 * 2.4596

FV = $36,894.05

QUESTION 5A -2

FV = $200,000 , r = 9%, t = 7 years

PV = 200,000/e^{(9% * 7)}

PV = 200,000/1.8776

PV = $106,518.4

QUESTION 5A -3

PV = $1000, t = 2 years

For Bank A, r = 7%

FV = 1000 * e^{(7% * 2)}

FV (A) = 1000 * 1.15027 = $1,150.27

For Bank B, r = 6.9%

FV = 1000 * e^{(6.9% * 2)}

FV (B) = 1000 * 1.14798 = $1,147.98

Difference FV(A) - FV (B) = 1150.27 - 1147.98 = $2.29

QUESTION 5A -4

40000 = 20000 * e^{(r * 6)}

2 = e^(6r)

Taking log on both sices {remember, Ln(e^x) = x}

ln(2) = 6r

r = 11.55%