Math 125 finite and modeling

Question

What monthly payment is needed for annuity to reach $25,000 over 15 years if you

earn 8.5% interest?

Answer 1

PMT = A x (APR/n) / [(1 + APR/n)^(nY) -1] where A is the target value $25,000, APR = 0.085, n = 12, Y = 15 yrs

PMT = 25000(0.085/12) / [(1 + 0.085/12)¹⁸⁰ - 1] 0.085/12 = 0.007083

PMT = 25000(0.007083) / [1.007083¹⁸⁰ - 1]

PMT = 177.075 / (3.56244 - 1) → 177.075 / 2.56244 ≅ $69.10/mo.

So you pay in a total of $69.10 x 180 = $12,438, or about half of the final value. The rest comes from interest.