Question

Your grandmother is gifting you $150 a month for four years while you attend college to earn your bachelor's degree. At a 3.7 percent discount rate, what are these payments worth to you on the day you enter college?

Answer 1

Present Value of an Ordinary Annuity

Monthly Payment (P) = $150 per month

Monthly Interest Rate (r) = 0.308333% per month [3.70% / 12 Months]

Number of period (n) = 48 Months [4 Years x 12 Months]

Therefore, the Present Value of an Ordinary Annuity = P x [{1 - (1 / (1 + r) n} / r]

= $150 x [{1 - (1 / (1 + 0.00308333)⁴⁸} / 0.00308333]

= $150 x [{1 - (1 / 1.159249)} / 0.00308333]

= $150 x [(1 - 0.862628) / 0.00308333]

= $150 x [0.137372 / 0.00308333]

= $150 x 44.553239

= $6,682.99

“Therefore, the present worth of the annuity payment will be $6,682.99”