Question

A 4-year annuity of eight $9,800 semiannual payments will begin 7 years from now, with the first payment coming 7.5 years from now.

a. If the discount rate is 7 percent compounded monthly, what is the value of this annuity five years from now? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

b. If the discount rate is 7 percent compounded monthly, what is the value three years from now? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

c. If the discount rate is 7 percent compounded monthly, what is the current value of the annuity? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

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Answer 1

It is given that monthly interest rate is (7% ÷ 12), whereas payments are made semi-annually.

The calculation of semi-annual interest rate is given below:

The formula to calculate present value of annuity at 7-year point from today is given below:

Substitute $9,800 for C, 0.0355 for i and 8 for n.

a.

The value calculated above is at time 7 and to calculate the value at time 5, the value must be discounted back for 4 semi-annual periods.

The value of annuity five years from today is calculated below:

b.

The value calculated above is at time 7 and to calculate the value at time 3, the value must be discounted back for 8 semi-annual periods.

The value of annuity three years from today is calculated below:

c.

The value calculated above is at time 7 and to calculate the value at time 0, the value must be discounted back for 14 semi-annual periods.

The value of annuity today is calculated below: