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Suppose you are going to receive $13,700 per year for six years. The appropriate interest rate is 8.6 percent.a-1 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)) Present value $
a-2 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)) Present value $
b-1 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)) Future value $ b-2 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))

Sagot :

Answer:

a-1 Present value = $62,196.97

a-2 Present value = $67,545.91

b-1 Future value = $102,034.77

b-2 Future value = $110,809.76

Explanation:

Let:

P = Annual amount = $13,700

r = Annual interest rate = 8.6%, or 0.086

n = number of years = 6

Therefore, we have:

a-1 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))

This can be calculated using the formula for calculating the present value of an ordinary annuity as follows:

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

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

Present value = $13,700 * ((1 - (1 / (1 + 0.086))^6) / 0.086)

Present value = $13,700 * 4.53992511948198

Present value = $62,196.97

a-2 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))

This can be calculated using the formula for calculating the present value of an annuity due as follows:

Present value = P * ((1 - [1 / (1+r))^n) / r) * (1+r) …………………………………. (2)

Substitute the values into equation (2), we have:

Present value = $13,700 * ((1 - (1 / (1 + 0.086))^6) / 0.086) * (1 + 0.086)

Present value = $13,700 * 4.53992511948198 * 1.086

Present value = $67,545.91

b-1 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))

This can be calculated using the formula for calculating the Future Value (FV) of an Ordinary Annuity as follows:

Future value = P * (((1 + r)^n - 1) / r) ................................. (3)

Substitute the values into equation (3), we have:

Future value = $13,700 * (((1 + 0.086)^6 - 1) / 0.086)

Future value = $13,700 * 7.44779374916618

Future value = $102,034.77

b-2 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))

This can be calculated using the formula for calculating the Future Value (FV) of an Annuity due as follows:

Future value = P * (((1 + r)^n - 1) / r) * (1 + r) ................................. (4)

Substitute the values into equation (4), we have:

Future value = $13,700 * (((1 + 0.086)^6 - 1) / 0.086) * (1 + 0.086)

Future value = $13,700 * 7.44779374916618 * 1.086

Future value = $110,809.76

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