You have decided to put $130 in a savings account at the end of each month. The savings account credits interest monthly, at the annual rate of 6%. How much money is in your account after 6 years?

You have decided to put $130 in a savings account at the end of each month. The savings account credits interest monthly, at the annual rate of 6%. How much money is in your account after 6 years?

Solution

monthly rate of interest  = 6%/12 = 0.005

Number of months = 6 x 12 = 72

Deposit made at the end of each month so, Number of years = 72-1 = 71

S = 130 (1.005)^71 + 130 (1.005)^70+ …….+130 (1.005)

Here , a=130 (1.005)^71 and x = 1/1.005

 

FV = 130+[130 (1.005)^71 [1-(1/1/1.005^71)] / 1-1/1.005 ]

Now, 1/1.005^71 = 1.005^-71 (Simple math)

FV = 130+130 (1.005)^71 [1-1.005^-71]/1-1.005^-1

FV = 11,233.15

Cincinnati Company has decided to put $30,000 per quarter in a pension fund. The fund will earn interest at the rate of 6% per year, compounded quarterly. Find the amount available in this fund after 10 years.

Cincinnati Company has decided to put $30,000 per quarter in a pension fund. The fund will earn interest at the rate of 6% per year, compounded quarterly. Find the amount available in this fund after 10 years. 

Answer

Solution

monthly rate of interest  = 6%/4 = 0.015

Number of months = 10 x4 = 40

S = 30,000 (1.015)^40 + 30,000  (1.015)^39+ …….+30,000 (1.015)

Here , a=30,000 (1.015)^40 and x = 1/1.015

FV = 30,000 (1.015)^40 [1-(1/1/1.015^40)] / 1-1/1.015

Now, 1/1.015^40 = 1.015^-40 (Simple math)

FV = 30,000 (1.015)^40 [1-1.015^-40]/1-1.015^-1

FV = 1,652,457

Suppose you have decided to put $200 at the beginning of every month in a savings account that credits interest at the annual rate of 6%, but compounds it monthly. Find the amount in this account after 30 years.

 Suppose you have decided to put $200 at the beginning of every month in a savings account that credits interest at the annual rate of 6%, but compounds it monthly. Find the amount in this account after 30 years.

Answer

monthly rate of interest  = 6%/12 = 0.005

Number of months = 30 x 12 = 360

S = 200 (1.005)^360 + 200 (1.005)^359+ …….+200 (1.005)

Here , a=200 (1.005)^360 and x = 1/1.005

 

FV = 200 (1.005)^360 [1-(1/1/1.005^360)] / 1-1/1.005

Now, 1/1.005^360 = 1.005^-360 (Simple math)

FV = 200 (1.005)^360 [1-1.005^-360]/1-1.005^-1

FV = 201,907.52

You decide to put $10,000 in a money market fund that pays interest at the annual rate of 7.2%, compounding it monthly. You plan to take the money out after one year and pay the income tax on the interest earned. You are in the 25% tax bracket. Find the total amount available to you after taxes.

 You decide to put $10,000 in a money market fund that pays interest at the annual rate of 7.2%, compounding it monthly. You plan to take the money out after one year and pay the income tax on the interest earned. You are in the 25% tax bracket. Find the total amount available to you after taxes.

Answer

Interest rate = 7.2%/ 12 = 0.006

FV = 10,000 x (1.006)^12 = 10744.24

The interest earned = 10744.24-10,000=744.24

You have to pay 25% tax on this amount.

Thus after paying taxes, it becomes = 744.24 x (1-0.25) = 558.18

Total amount available after 12 months = 10,000 + 558.18 =10,558.18

Compute the present value of a $150 cash flow for the following combinations of discount rates and times: (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Compute the present value of a $150 cash flow for the following combinations of discount rates and times: (Do not round intermediate calculations. Round your answers to 2 decimal places.)

	Present Value
a. r = 12%, t = 8 years	$
b. r = 12%, t = 16 years
c. r = 6%, t = 8 years
d. r = 6%, t = 16 years

Explanation:

a. $150/(1.12)8 = $60.58

b. $150/(1.12)16 = $24.47

c. $150/(1.06)8 = $94.11

d. $150/(1.06)16 = $59.05

Compute the future value of a $150 cash flow for the same combinations of rates and times: (Do not round intermediate calculations. Round your answers to 2 decimal places.)

	Future Value
a. r = 12%, t = 8 years	$
b. r = 12%, t = 16 years
c. r = 6%, t = 8 years
d. r = 6%, t = 16 years

Explanation:

a. $150 × (1.12)8 = $371.39

b. $150 × (1.12)16 = $919.56

c. $150 × (1.06)8 = $239.08

d. $150 × (1.06)16 = $381.05

In 1880 five aboriginal trackers were each promised the equivalent of 100 Australian dollars for helping to capture the notorious outlaw Ned Kelley. In 1994 the granddaughters of two of the trackers claimed that this reward had not been paid. The Victorian prime minister stated that if this was true, the government would be happy to pay the $100. However, the granddaughters also claimed that they were entitled to compound interest.

a.	How much was each entitled to if the interest rate was 3%? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Future value

$

b.	How much was each entitled to if the interest rate was 6%? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Future value

$

Explanation:

a.

$100 × (1.03)114 = $2,906.99

b.

$100 × (1.06)114 = $76,712.94

a-1.	Calculate the present value of an annual payment of $900 you would received for 12 years if the interest rate is 3%. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Present value

$

a-2.	Calculate the present value of an annual payment of $700 you would received for 17 years if the interest rate is 3%. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Present value

$

a-3.	Which option would you prefer?
	$700 a year for 17 years

b-1.	Calculate the present value of an annual payment of $900 you would received for 12 years if the interest rate is 12%. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Present value

$

b-2.	Calculate the present value of an annual payment of $700 you would received for 17 years if the interest rate is 12%. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Present value

$

b-3.	Which option would you prefer?
	$900 a year for 12 years

rev: 01_28_2012


Explanation:

You should compare the present values of the two annuities.