Question

1. Find the present value of the annuity given the following. a) 36 monthly payments of $250 in an account where the interest rate is 3.5% compounded monthly.

PMT = 250, i = 0.035/12= 0.002916, n = 36 X 12 = 36

?? = ( 250[1-(1+0.002916)-342])/0.002916

PV = ( 24.879080)/0.002916

PV = 8531.920438 = $8,531.90

b) 60 weekly payments of $125 in an account where the interest rate is 5% compounded weekly.

PMT = 125, i = 0.05/52= 0.000961, n = 60x 52= 3120

?? = 125[1-(1+0.000961)^-60  /0.000961

PV = 7.000377/0.000961

PV = $7284.47138397 = $7284.48

Is this correct ?

Answer 1

Solution

PV of annuity= Annuity amount*[(1-(1/(1+r)^n))/r]

where r= Annual interest rate

n= number of years

In case of monthly compounding the formula will be

PV of annuity= Annuity amount*[(1-(1/(1+r/12)^(12*n)))/(r/12)]

a. Putting values in the formula

PV= 250*[(1-(1/(1+.035/12)^(12*3)))/(.035/12)]

=8531.818

b. Here [ayment and compounding is weekly

PV of annuity= Annuity amount*[(1-(1/(1+r/52)^(52*n)))/(r/52)]

Here 52 used as there are 52 weks in year

PV of annuity=125*[(1-(1/(1+.05/52)^(60)))/(.05/52)]

=7284.35353