A 9-year annuity of eighteen $6,015 semiannual payments will begin 10 years from

Question

A 9-year annuity of eighteen $6,015 semiannual payments will begin 10 years from now, with the first payment coming 10.5 years from now.

If the discount rate is 11 percent compounded monthly, what is the value of this annuity five years from now? (Do not round intermediate calculations and round your final answer to 2 decimal places (e.g., 32.16).)

If the discount rate is 11 percent compounded monthly, what is the value three years from now? (Do not round intermediate calculations and round your final answer to 2 decimal places (e.g., 32.16).)

If the discount rate is 11 percent compounded monthly, what is the current value of the annuity? (Do not round intermediate calculations and round your final answer to 2 decimal places (e.g., 32.16).)

A 9-year annuity of eighteen $6,015 semiannual payments will begin 10 years from now, with the first payment coming 10.5 years from now.

Explanation / Answer

Interest rate is give in APR. So, the monthly interest rate is as follows

Monthly rate = .11 / 12 = .00916

Now we can use EAR equation for calculationg effective semiannual rate.

Semiannual rate = (1.00916)6 – 1

Semiannual rate = 0.0563 or 5.63%

So, The PV of the annuity as follow....

PVA @ year 10 = $6,015{[1 – (1 / 1.0563)18] / .0563}

PVA @ year 10 = $66,976.64

PV @ year 5 = $66,976.64 / 1.05636

PV @ year 5 = $48,216.95

Calculation of EAR as follow...

EAR = (1 + .0091)12 – 1

EAR = 0.1148 or 11.48%

Value of the annuity at one time as follow....

PV @ year 3 = $53,776.72 / 1.056310 = $31,097.22

PV @ year 3 = $53,776.72 / 1.11485 = $31,232.70

PV @ year 0 = $53,776.72 / 1.056320 = $17,982.45

PV @ year 0 =$53,776.72 / 1.114810 = $18,139.48

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