Question

A 5-year annuity of ten $7,800 semiannual payments will begin 9 years from now, with the first payment coming 9.5 years from now. The discount rate is 13 percent compounded monthly.

a. 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. 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. 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.)

Answer 1

First we need to calculate the value of annuity at 9th Year from now.

Here we have

PMT = $7800

Rate = 13/2= 6.5% as it compounded semi annually

N=5*2 = 10 as it is compounded semi annually

PV= PMT*((1-(1+r)^-n)/r)

=7800*((1-1.065^-10)/0.065

=7800*((1-0.5327)/0.065)

= 7800*7.189= $56074.20

A. Now we need to discount it back to 4 years from 9th Year

PV= FV/(1+r)^n

56074.20/(1.0065^4)

= $43587.77

B.Now we need to discount it back to 6 years from 9th Year

PV= FV/(1+r)^n

56074.20/(1.0065^6)

= $38429.56

C. Now we need to discount it back to 9 years from 9th Year

PV= FV/(1+r)^n

56074.20/(1.0065^9)

= $31813.38