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A 6-year annuity of twelve $6,185 semiannual payments will begin 11 years from now, with the...

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 $

Solutions

Expert Solution

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


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