Question

You plan to spend a semester abroad in France. You will live in France for 8 months starting 9 months from now. Each month in France will cost you $6,515 How much must you invest each month, for 5 months, starting next month to exactly pay for your trip if your investments earn 3.63% APR (compounded monthly)?

Answer 1

Rent will be paid in advance.

PV for rent annuity(8 months from now) = Monthly Payment * [{1 - (1 + r)^-n} / r]

= $6,515 * [{1 - (1 + 0.0363/12)^-8} / (0.0363/12)]

= $6,515 * [0.0239 / 0.003025]

= $6,515 * 7.8922

= $51,417.61

PV of rent annuity(5 months from now) = PV for rent annuity(8 months from now) /

(1 + r)ⁿ

= $51,417.61 / [1 + (0.0363/12)]^(8-5)

= $51,417.61 / 1.0091 = $50,953.81

Monthy Investment = [PV for rent annuity(5 months from now) * r] / [(1 + r)ⁿ - 1]

= [$50,953.81 * (0.0363/12)] / [{1 + (0.0363/12)}⁵ - 1]

= $154.14 / 0.0152

= $10,129.29