Using annual semiannual and quarterly compounding periods 1

Using? annual, semiannual, and quarterly compounding? periods, (1) calculate the future value if???$9,000is deposited initially at 11?%annual interest for7years, and? (2) determine the effective annual rate.

Solution

1.

For annual compounding

Using financial calculator BA II Plus - Input details:

#

I/Y = Rate / Frequency of compounding =

11.000000

PMT = Payment or Coupon or Regular payments / Frequency =

$0.00

N = Total number of periods = Number of years x frequency =

7

PV = Present Value =

-$9,000.00

CPT > FV = Future Value for annual interest rate =

$18,685.44

For semiannual compounding

Using financial calculator BA II Plus - Input details:

#

I/Y = Rate / Frequency of compounding =

5.500000

PMT = Payment or Coupon or Regular payments / Frequency =

$0.00

N = Total number of periods = Number of years x frequency =

14

PV = Present Value =

-$9,000.00

CPT > FV = Future Value for semiannual =

$19,044.82

For quarterly compounding

Using financial calculator BA II Plus - Input details:

#

I/Y = Rate / Frequency of compounding =

2.750000

PMT = Payment or Coupon or Regular payments / Frequency =

$0.00

N = Total number of periods = Number of years x frequency =

28

PV = Present Value =

-$9,000.00

CPT > FV = Future Value for quarterly compounding rate =

$19,236.84

-----------------

2.

EAR = (1+Rate/Compounding frequency)^Compounding frequency - 1

Effective annual rate for annual compounding = (1+11%/1)^1 -1 = 11.00%

Effective annual rate for semiannual compounding = (1+11%/2)^2 -1 = 11.30%

Effective annual rate for semiannual compounding = (1+11%/4)^4 -1 = 11.46%