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

The U.S. government fixed the price of gold at $35 an oz in 1934. In 2005, the price of the yellow metal was $480 an oz. Calculate the price appreciation of gold as percent per year, compounded annually.

 The U.S. government fixed the price of gold at $35 an oz in 1934. In 2005, the price of the yellow metal was $480 an oz. Calculate the price appreciation of gold as percent per year, compounded annually.

Answer

Number of years = n = 2005 - 1934 = 71 years

Present Value = 35, Future Value = 480 , rate =r=?

Here is our formula,

Future Value = Present Value x (1+r)^n

We need to put above values, we get

480 = 35 (1+r)^71

480/35 = (1+r)^71

13.71 =(1+r)^71

Now, we need to take 1/71 power both sides, we get 

(13.71)^1/71 = (1+r)^71x1/71

1.037568 = 1+r

r = 1.037568 -1 

r = 0.037568 

r = 3.757%

If we use Excel, then we find it very easily, we used rate formula in excel.

Your employer has promised to give you a $5,000 bonus after you have been working for him for 5 years. What is the present value of this bonus if the proper discount rate is 8%?

 Your employer has promised to give you a $5,000 bonus after you have been working for him for 5 years. What is the present value of this bonus if the proper discount rate is 8%?

Answer

Present value = 5000 x (1.08)^-8 = 3402.92

Ahsan Co bought a piece of land in 1991 for $160,000 which appreciated in value at the rate of 3% per year for the first three years and then at the rate of 4% for the next four years. Find its value after 7 years.

 Ahsan Co bought a piece of land in 1991 for $160,000 which appreciated in value at the rate of 3% per year for the first three years and then at the rate of 4% for the next four years. Find its value after 7 years.

Answer

Land Value for first 3 years = 160,000 x (1.03)^3 = 174836.30

So,

Land Value for next 4 years = 174836.30 x (1.04)^4 = 204,533. 80

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