Question

I'm struggling with this questions from a Finance course. Can you please provide the details of the answer.

Your parents plan to give you $200 a month for four years while you are in college. At a discount rate of 6 percent, compounded monthly, what are these payments worth to you when you first start college?

Answer 1

The worth of the payments made at the start of the college is the Present Value of the ordinary annuity and it is calculated by using the following formula

Monthly Payment (P) = $200 per month

Monthly Interest Rate (r) = 0.50% [6% / 12 months]

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

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

= $200 x [{1 - (1 / (1 + 0.005)⁴⁸} / 0.005]

= $200 x [{1 - (1 / 1.270489)} / 0.005]

= $200 x [(1 - 0.787098) / 0.005]

= $200 x [0.212902 / 0.005]

= $200 x 42.580318

= $8,516.06

“Therefore, the worth of the payments will be $8,516.06”