Suppose you are going to receive $14,000 per year for six years. The appropriate

Question

Suppose you are going to receive $14,000 per year for six years. The appropriate interest rate is 8.9 percent.

   

What is the present value of the payments if they are in the form of an ordinary annuity? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

  

  

What is the present value if the payments are an annuity due? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

  

  

Suppose you plan to invest the payments for six years. What is the future value if the payments are an ordinary annuity? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

  

Suppose you plan to invest the payments for six years. What is the future value if the payments are an annuity due? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

  

Suppose you are going to receive $14,000 per year for six years. The appropriate interest rate is 8.9 percent.

Explanation / Answer

a1. ordinary annuity means payment being made at the end of year. Pv of annuity at the end of year 1 = amount/(1+interest rate)^1. at the end of year 2 = amount/(1+interest rate)^2 and so on.

This formula has been used in the table below to calculate the PV of annuities:

Hence the present value = $62,990.55

a2. annuity due means payment is being made at the beginning of the year. so pv for year 1 will be = the amount itself. for year 2 = amount/(1+r)^1. for year 3 = amount/(1+r)^2.

The formula has been used in the table below:

So PV = $68,596.71

B1. If investing 14,000 at the end of each year, for 6 years, the future value at the end of 6 years formula will be - for year 1 = amount*(1+r)^(6-1). for year 2 = amount*(1+r)^(6-2)..... till 6th year

So, FV will be $105,061.27

b2 - FV, in case of annuity due will be: for 1st year = amount*(1+r)^6. for 2nd year = amount*(1+r)^5...... till 6th year.

So, FV will be $114,411.73

Year Amount Interest rate PV 1 14,000.00 0.089 12,855.83 2 14,000.00 11,805.17 3 14,000.00 10,840.38 4 14,000.00 9,954.43 5 14,000.00 9,140.89 6 14,000.00 8,393.84 Total 62,990.55

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