Question

Decimals are extremely important in this question. Do not round until your final answer and provide 4 decimals in your final answer. What is the future value of $1,000 one year from now if it is compounded at:

a) a 12% annual rate compounded annually?

b) 12% annual rate compounded quarterly?

c) 12% annual rate compounded monthly?

d) 12% annual rate compounded daily (assume a 365 day year)?

Answer 1

(a) Initial Deposit = $ 1000

Nominal Annual Rate = 12 %, Compounding Frequency: n = 1

Applicable Periodic Interest Rate = (12/n) = 12/ 1 = 12%

Tenure = 1 year

Future Value = 1000 x (1.12) = $ 1120

(b)

Initial Deposit = $ 1000

Nominal Annual Rate = 12 %, Compounding Frequency: n = 4

Applicable Periodic Interest Rate = (12/n) = 12/ 4 = 3%

Tenure = 1 year or 4 quarters

Future Value = 1000 x (1.03)^(4) = $ 1125.51

(c)

Initial Deposit = $ 1000

Nominal Annual Rate = 12 %, Compounding Frequency: n = 12

Applicable Periodic Interest Rate = (12/n) = 12/ 12 = 1%

Tenure = 1 year or 12 months

Future Value = 1000 x (1.01)^(12) = $1126.83

(d)

Initial Deposit = $ 1000

Nominal Annual Rate = 12 %, Compounding Frequency: n = 365 days

Applicable Periodic Interest Rate = (12/n) = 12/ 365 =

Tenure = 1 year or 365 days

Future Value = 1000 x (1.0003288)^(365) = $ 1127.47