Instead of setting up a trust fund, assume Erin’s grandmother wants to give her
ID: 2770093 • Letter: I
Question
Instead of setting up a trust fund, assume Erin’s grandmother wants to give her an amount on her 18th birthday that will allow her to withdraw $2,000 each of the next four years. The series of four equal payments or receipts that occur at evenly spaced intervals is called an annuity.
Notice that the website below provides a place for you to determine the present value of an annuity.
http://www.investopedia.com/calculator/annuitypv.aspx
Assume the grandmother’s initial lump sum given on the 18th birthday will still be invested at 10% compounded annually. (After the first $2,000 is withdrawn, the remaining funds will still be invested earning 10%).
a.How much should Grandma initially invest at 10%
b.Is the initial investment more or less than the $8,000 Erin will withdraw? Why?
Explanation / Answer
a.
PV = Pmt x ((1-((1+r/n)-nt )) / r)
Payment per period (PMT) = $2,000
Discount Rate Per period = 10%
Number of Compounding per year (n) = 1
t = 4 Years
PV = $2,000 x ((1-(1 + 0.10)-4)/0.10 = $6,339.73
b. The initial investmet is less than $8,000 as it will earn an interest which will increase the money.