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- May 23, 2018

Week Four Discussion: Initial Investment I want to plan a trip to India in the near future with my partner to see the world famous Taj Mahal and other historical places in India. I have done a little research that we will need around $40,000 for the trip. I want to this trip in 12 years from now. I have also done research about this investment and found an investment opportunity, which promises to have an average annual return of about 8% annually if I choose their long-term investment plan. Now, I want to know how much I need to invest in this plan today to have $40,000 in 12 years.

The desired item is travel.

The cost in 12 years will be about $40,000.

The average annual interest rate of the investment is 8%.

The Present Value formula is given by:

P = A(1 + r)-n

Where P is the present value that will amount to A dollar in n years at interest rate r compounded annually. The value of r is taken in decimal in this formula.

In this formula, the base quantity (1 + r) is raised to a power of –n that is a negative exponent. If we apply the rules of exponent, than the base quantity (1 + r) will change position and go down to the denominator and will be raised to the power of n. Now this will divide A instead of multiplying for calculating present value P.

P = A(1 + r)-n

P = 40000(1 + 0.08)-12 Plugging relevant numbers into the formula.

P = 40000(1.08)-12 Adding inside the parenthesis

P = 40000 / (1.08)12 The negative exponent creates the reciprocal of the base number. It changes its position and goes down in the denominator with positive exponent to the base.

P = 40000 / 2.518170 Applying exponent to the base number

P = $15,884.55 Dividing the numerator by the denominator

Thus, I will need around $16,000 to invest today in the long-term investment plan that gives an average annual return on investment of about 8% to have around $40,000 in 12 years for my trip. This suggests that because of inflation, what we will get today in around $16,000, will get in around $40,000 in 12 years.

The present value formula is similar to the exponential decay formula. The exponential decay formula is given by:

N = N0ekt where k < 0

In this formula, N0 is the initial population (or quantity), N is the population (or quantity) after time t and k is a constant, which has a negative value.

Now if we compare above formula to the present value formula P = A(1 + r)-n, N is equivalent to P, N0 is equivalent to A, e is equivalent to (1 + r) and kt is equivalent to –n.

The desired item is travel.

The cost in 12 years will be about $40,000.

The average annual interest rate of the investment is 8%.

The Present Value formula is given by:

P = A(1 + r)-n

Where P is the present value that will amount to A dollar in n years at interest rate r compounded annually. The value of r is taken in decimal in this formula.

In this formula, the base quantity (1 + r) is raised to a power of –n that is a negative exponent. If we apply the rules of exponent, than the base quantity (1 + r) will change position and go down to the denominator and will be raised to the power of n. Now this will divide A instead of multiplying for calculating present value P.

P = A(1 + r)-n

P = 40000(1 + 0.08)-12 Plugging relevant numbers into the formula.

P = 40000(1.08)-12 Adding inside the parenthesis

P = 40000 / (1.08)12 The negative exponent creates the reciprocal of the base number. It changes its position and goes down in the denominator with positive exponent to the base.

P = 40000 / 2.518170 Applying exponent to the base number

P = $15,884.55 Dividing the numerator by the denominator

Thus, I will need around $16,000 to invest today in the long-term investment plan that gives an average annual return on investment of about 8% to have around $40,000 in 12 years for my trip. This suggests that because of inflation, what we will get today in around $16,000, will get in around $40,000 in 12 years.

The present value formula is similar to the exponential decay formula. The exponential decay formula is given by:

N = N0ekt where k < 0

In this formula, N0 is the initial population (or quantity), N is the population (or quantity) after time t and k is a constant, which has a negative value.

Now if we compare above formula to the present value formula P = A(1 + r)-n, N is equivalent to P, N0 is equivalent to A, e is equivalent to (1 + r) and kt is equivalent to –n.