Question

You plan to spend a semester abroad in France. You will live in France for 10 months starting 9 months from now. Each month in France will cost you $7,829 How much must you invest each month, for 4 months, starting next month to exactly pay for your trip if your investments earn 3.46% APR (compounded monthly)?

Answer 1

Amount Required after 9 Months:

Assuming spending s are Month end.

PV of Annuity:

Annuity is series of cash flows that are deposited at regular intervals for specific period of time. Here cash flows are happened at the end of the period. PV of annuity is current value of cash flows to be received at regular intervals discounted at specified int rate or discount rate to current date.

PV of Annuity = Cash Flow * [ 1 - [(1+r)^-n]] /r
r - Int rate per period
n - No. of periods

Particulars	Amount
Cash Flow	$            7,829.00
Int Rate	0.2883%
Periods	10

PV of Annuity = Cash Flow * [ 1 - [(1+r)^-n]] /r
= $ 7829 * [ 1 - [(1+0.0029)^-10]] /0.0029
= $ 7829 * [ 1 - [(1.0029)^-10]] /0.0029
= $ 7829 * [ 1 - [0.9716]] /0.0029
= $ 7829 * [0.0284]] /0.0029
= $ 77062.64

Amount Required Today:

Present Value:

Present value is current value of Future cash flows discounted at specified discount Rate.

PV = FV / (1+r)^n
Where r is Int rate per period
n - No. of periods

Particulars	Amount
Future Value	$            77,062.64
Int Rate	0.2883%
Periods	9

Present Value = Future Value / ( 1 + r )^n
= $ 77062.64 / ( 1 + 0.0029 ) ^ 9
= $ 77062.64 / ( 1.0029 ) ^ 9
= $ 77062.64 / 1.0263
= $ 75091.39