Question

"Seamus McIntyre started saving for retirement today by investing $384 in an account earning 0.0879. He plans to continue with monthly contributions of the same amount for 30 years. The present value of his investment is":

Answer 1

Since investment is starting today, this investment is in the form of annuity due.

present value of annuity due = A + A[1 -(1+r)^-(n-1)]/r

here,

A=384

r =0.0879 per year =>0.0879/12 =>0.007325 per month.

n = 30 years -12 months=>360

n-1=>360-1=>359.

384 + 384*[1-(1.007325)^-(359)]/0.007325

=>384+384*[0.9272037/0.007325]

=>384+(384*126.58071)

=>384+48,606.99264

=>$48,990.99. or $48,991....(if rounded to nearest dollar).