Interest question Actuarial Science An annuity pays 1200 per

Interest question: Actuarial Science

An annuity pays $1200 per quarter for 5 years with the first payment on April 1, 2015. Given an annual effective rate of interest of 5.2%

a) Find the PV on 4/1/2015

b) Find the AV on 1/1/2020.

PV of annuity due = A*[1-(1+i)^-n] / i*(1+i)

Here A = 1200

I = 5.2% p.a or 1.3% quarterly compounding

N = 5 years or 20 periods

PV on 4/1/2015 = 1200*[1-(1+1.3%)^-20]/1.3%*(1+1.3%)

= $21,287.53

AV of annuity due = A*[(1+i)^n-1] / i*(1+i)

Here A= 1200

I = 5.2% p.a or 1.3% quarterly compounding

N = 4 year 9 months or 19 periods

AV on 1/1/2020 = 1200*[(1+1.3%)^19-1]/1.3%*(1+1.3%)

=$26,008.51