The present value of an annuity that pays $100 every 6 months for 5 years is $808.38
What is the equivalent semiannual interest rate in this case?
The equivalent semiannual interest rate for 8.0% compounded monthly can be determined by converting the monthly compounding interest rate to a semiannual compounding rate as shown below:
(1+APR/12)^12=(1+APR/2)^2
APR with 12 compounding periods is 8.0%(every month 12 times a year)
APR with 2 compounding periods a year(semiannually) is unknown
(1+8.0%/12)^12=(1+APR/2)^2
1.08299950680751=(1+APR/2)^2
(1.08299950680751)^1=(1+APR/2)^2
divide indexes on both sides by 2
(1.08299950680751)^(1/2)=1+APR/2
APR/2=(1.08299950680751)^(1/2)-1
APR/2=APR compounded semiannually/2=semiannual interest rate=0.0406726223013221
The present value of the annuity can be determined using the below present value formula of an ordinary annuity:
PV=PMT*(1-(1+r)^-N/r
PMT=semiannual payment=$100
r=semiannual interest rate=0.0406726223013221
N=number of semiannual payments in 5 years=5*2=10
PV=$100*(1-(1+0.0406726223013221)^-10/0.0406726223013221
PV=$808.38
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