# Solved Question: A 6-year annuity of twelve \$6,185 semiannual payments will begin

## Description

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?

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

## Reviews

There are no reviews yet.