A fifteen-year annuity pays $1400 + 300k on the first day of the k ? th month of

Question

A fifteen-year annuity pays $1400 + 300k on the first day of the k ? th month of the year. Thus it pays $1700 each January 1, $2000 each February 1,..., $5000 each December 1. The first payment is on a January 1. Find an expression for the value of this annuity just before the first payment and evaluate it if the annual effective interest rate is 3%.

a. 16800a ?(15)+43200(I(12)a)(12)(1+i)12a ?15i. This is approximately 380606.59 when i 12i 1

b. 16800a ?(12)+43200(I(12)a)(15)(1+i)12a ?15i. This is approximately 490985.12 when i = 3%

c. 16800a ?(12)+43200(I(12)a)(12)(1+i)12a ?15i. This is approximately 486386.33 when i = 3%

d. 16800a ?(15)+43200(I(12)a)(12)(1+i)12a ?12i. This is approximately 455037.76 when i = 3%

e. 16800a ?(12)+43200(I(12)a)(15)(1+i)15a ?15i. This is approximately 690803.11 when i= 3%

Explanation / Answer

c. 16800a ?(12)+43200(I(12)a)(12)(1+i)12a ?15i. This is approximately 486386.33 when i = 3%

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