Veronica purchases a retirement annuity that will pay her $2,000 at the end of every six months for the first eleven years and $800 at the end of every month for the next five years. The annuity earns interest at a rate of 2% compounded quarterly.

a)What was the purchase price of the annuity?

b) How much interest did Veronica receive from the annuity?

Please see explanation for your solution.thank you

Step-by-step explanation

1.
Rate compounded monthly = [(1 + (2%/4))^(4/12) - 1] * 12 

= 1.99667589517

= 2%

Purchase price 

= 2000/(1 + r/12)^6 * (1 - 1/(1 + r/12)^132)/(1 - 1/(1 + r/12)^6) 

+ 800/(1 + r/12)^133 * (1 - 1/(1 + r/12)^60)/(1 - 1/(1 + r/12))

Purchase price 

= 2000/(1 + (2%/12))^6 * (1 - 1/(1 + (2%/12))^132)/(1 - 1/(1 + (2%/12))^6 + 800/(1 + (2%/12))^133 * (1 - 1/(1 + (2%/12))^60)/(1 - 1/(1 + (2%/12))

= (1980.11615009 * 0.1973342234)/0.00994192495 

+ (641.064180974 * 0.09508725938)/0.00166389351

= 39302.7190091 + 36635.1786873

= 75937.8976964

= 75937.90

2. interest receive
= 2000 * 11 * 2 + 800 * 12 * 5 - 75937.90
= 44000 + 48000 - 75937.90

= 16062.1