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Calculate the present value of the following: a-1. annual payment of $775 for 10 years at 4% interest. a-2. annual payment of $575 for 15 years at 4% interest. a-3. which option would you prefer? b-1. annual payment of $775 for 10 years at 16% interest. b-2. annual payment of $575 for 15 years at 16% interest. b-3. which option would you prefer?

User Grishka
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1 Answer

3 votes

Answer:

Option "b-2" has a higher present value, making it the preferred option.

Explanation:

To calculate the present value of the cash flows, we can use the formula for the present value of an annuity:

PV = C * (1 - (1 + r)^(-n)) / r

Where:

PV is the present value

C is the annual payment

r is the interest rate per period

n is the number of periods

Let's calculate the present value for each option:

a-1. Annual payment of $775 for 10 years at 4% interest:

C = $775, r = 4%, n = 10

Using the formula, the present value is:

PV = 775 * (1 - (1 + 0.04)^(-10)) / 0.04 ≈ $6,668.71

a-2. Annual payment of $575 for 15 years at 4% interest:

C = $575, r = 4%, n = 15

Using the formula, the present value is:

PV = 575 * (1 - (1 + 0.04)^(-15)) / 0.04 ≈ $7,610.58

a-3. To determine which option is preferred, we compare the present values. In this case, option "a-2" has a higher present value, which means it is the preferred option.

b-1. Annual payment of $775 for 10 years at 16% interest:

C = $775, r = 16%, n = 10

Using the formula, the present value is:

PV = 775 * (1 - (1 + 0.16)^(-10)) / 0.16 ≈ $3,051.84

b-2. Annual payment of $575 for 15 years at 16% interest:

C = $575, r = 16%, n = 15

Using the formula, the present value is:

PV = 575 * (1 - (1 + 0.16)^(-15)) / 0.16 ≈ $4,699.35

b-3. Similarly, we compare the present values to determine the preferred option. In this case, option "b-2" has a higher present value, making it the preferred option.

To summarize:

Option "a-2" is preferred over option "a-1" at 4% interest.

Option "b-2" is preferred over option "b-1" at 16% interest.

Thus,

Option "b-2" has a higher present value, making it the preferred option.

User Hadi Mir
by
7.7k points
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