Question

A 6-year annuity of twelve $6,185 semiannual payments will begin 11 years from now, with the first payment coming 11.5 years from now. If the discount rate is 9 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.) Value of the annuity $ If the discount rate is 9 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.) Value of the annuity $ If the discount rate is 9 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.) Value of the annuity $

Answer 1

Discount rate=9% (0.09) compounded monthly

Semi annual interest rate=((1+(0.09/12))^6)-1=1.045852-1=0.045852

Present Value (PV) of payment=(Payment)/((1+i)^N)

i=0.045852, N=Period of payment

Payments and PV of payments are given below:

	N	A	B=A/(1.045852^N)
Years from now	Semi annual period	Payment	PV of payment
11.5	1	$6,185	5913.838669
12	2	$6,185	5654.565531
12.5	3	$6,185	5406.659385
13	4	$6,185	5169.621882
13.5	5	$6,185	4942.976522
14	6	$6,185	4726.267696
14.5	7	$6,185	4519.059768
15	8	$6,185	4320.936201
15.5	9	$6,185	4131.498722
16	10	$6,185	3950.366516
16.5	11	$6,185	3777.175467
17	12	$6,185	3611.577419
		TOTAL	56124.54378

Value of this annuity11 years from now=$56,124.54

Number of semi annual period from year 5 to year11=6*2=12

Value of annuity five years from now=$56,124.54378/(1.045852^12)= $ 32,772.54

Number of semi annual periods from 3 years to 5 years from now=4

Value of annuity three years from now= $ 32,772.54 /(1.045852^4)= $ 27,392.34

Number of semi annual period from now to 3 years=6

Current value of the annuity= $ 27,392.34/(1.045852^6)= $ 20,931.86