Question

your parents want to place money in an account so that you can withdraw $200 a week for the next four years while you finish college and graduate school they place the money in account that earns 4% interest compounded weekly how much do they need to place in the account so that the funds will be depleted in four years years assume that you will make the First withdrawal 1 week from today​

Answer 1

They need to place $38,428.99

Step-by-step explanation:

First, this is an annuity-type of question since there are recurring cashflow of $200.

Weekly PMT= 200

Weekly rate; r = 4%/52=0.076933% or 0.00076923 as a decimal.

Total duration( in weeks) = 4yrs * 52 = 208 weeks

Next, use present value of annuity formula to find PV;

PVA=
`(PMT)/(r) (1-(1+r)^(-n) )\\ \\ PVA= (200)/(0.00076923) (1-(1+0.00076923)^(-208) )`

PVA= 260,000.26*(0.1478038)

PVA= $38,428.99014

Therefore, they need to place $38,428.99