Question

You plan to visit France for 3 months, (starting next month). You will spend $8,412 in each of those months.
How much do you need to invest today to just fund your visit if your investments earn 2.86% APR (compounded monthly)?

Answer 1

visit of france will be started from next month and we will have to calculate the amount now means what we compute the amount now can get one month interest over it of one month and then the amount started to expense.

so as per formula of payout annuity P0 =d*[(1 - (1+r/k)^(-n*k)]/(r/k)

where P0 is the balance in the account at the beginning

d is the regular withdrawl = $ 8412

r is the annual interest rate = 2.86%

k is the number of compounding periods in a year = 12 as compounded monthly

n is the number of years we plan to take withdrawls = 3months

put all the values in above formulae

P0 = 8412*[1 - (1+0.0286/12)^(-1/4*12)]/(0.0286/12)

= 3529510*[1 - (1+0.002383)^(-3)]

= 3529510*[1 - 1.002383^(-3)]

= 3529510*[1 - 0.992884]

= 3529510*0.007116

= 25116.18

Please check with your answer and let me know.