# An exchange student wants to have $25/day spending money while in china. His parents set up an annuity @4%/a compounded daily for the year he is away. How much would they need to invest today to...

An exchange student wants to have $25/day spending money while in china. His parents set up an annuity @4%/a compounded daily for the year he is away. How much would they need to invest today to cover his needs, if he is leaving today?

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You need the amount invested at 4% compounded daily such that daily withdrawals of $25 results in a balance of $0 in 365 days.

The formula is `PV="PMT"(1-(1+r/m)^(-mt))/(r/m)` where PV is the present value (the amount invested originally), PMT is the regular payment or withdrawal, r is the interest rate, m is the number of compounding periods per year and t is the number of years.

PMT=25,i=.04,m=365,t=1

`PV=25(1-(1+.04/365)^(-365))/(.04/365)~~8944.43`

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The amount required is $8944.43

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Compare to the $9125 needed if not invested.

Using a TI-8X, you can use the TVM solver:

N=365

I=4

PMT=-25

FV=0

P/Y=365

C/Y=365

Then solve for PV to get 8944.428833