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Using the appropriate present value table and assuming a 12% annual interest rate, determine the present value on December 31, 2018, of a five-period annual annuity of $5,000 under each of the following situations: (FV of $1, PV of $1, FVA of $1, PVA of $1, FVAD of $1 and PVAD of $1) (Use appropriate factor(s) from the tables provided.)
1. The first payment is received on December 31, 2019, and interest is compounded annually.
2. The first payment is received on December 31, 2018, and interest is compounded annually.
3. The first payment is received on December 31, 2019, and interest is compounded quarterly.

Sagot :

Answer:

1. Present value on December 31, 2018 = $18,023.88

2. Present value on December 31, 2018 = $20,186.75

3. Present value on December 31, 2018 = $17,780.59

Explanation:

1. The first payment is received on December 31, 2019, and interest is compounded annually.

This is an example of ordinary annuity. Therefore, the present value on December 31, 2018 can be calculated using the formula for calculating the present value of an ordinary annuity as follows:

PV = P * ((1 - (1 / (1 + r))^n) / r) …………………………………. (1)

Where;

PV = present value on December 31, 2018 = ?

P = Annual annuity = $5,000

r = Annual interest rate = 12%, or 0.12

n = number of years = 5

Substitute the values into equation (1), we have:

PV = $5,000 * ((1 - (1 / (1 + 0.12))^5) / 0.12)

PV = $5,000 * 3.60477620234501

PV = $18,023.88

2. The first payment is received on December 31, 2018, and interest is compounded annually.

This is an example of annuity due. Therefore, the present value on December 31, 2018 can be calculated using the formula for calculating the present value of an annuity due as follows:

PV = P * ((1 - [1 / (1+r))^n) / r) * (1+r) .................................. (2)

Where;

Where;

PV = present value on December 31, 2018 = ?

P = Annual annuity = $5,000

r = Annual interest rate = 12%, or 0.12

n = number of years = 5

Substitute the values into equation (1), we have:

PV = $5,000 * ((1 - [1 / (1+0.12))^5) / 0.12) * (1+0.12)

PV = $5,000 * 3.60477620234501 * 1.12

PV = $5,000 * 4.03734934662641

PV = $20,186.75

3. The first payment is received on December 31, 2019, and interest is compounded quarterly.

Note: See the calculation of the present value on December 31, 2018 in the attached excel file.

This is also an example of ordinary annuity.

In the attached excel file, the following formula is used:

Discounting factor = 1 / (1 + r)^n .............. (1)

Where;

r = Quarterly interest rate = Annual interest rate / Number of quarters in a year = 12% / 4 = 0.12 / 4 = 0.03

n = number of quarters = number of years * Number of quarters in a year

From the attached excel file, we have:

Present value on December 31, 2018 = Total present value = $17,780.59

View image amcool
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