Annuity payment help?
I’m stuck on this question and can’t figure out the formula.. does anyone know how to calculate? Please help..
How much money must be deposited now, at 6% interest, compounded semiannually, to yield an annuity payment of $4000 at the beginning of each six-month period, for a total of five years?
Thanks!
Let:
s be the sum deposited,
a be the amount of $1 at the end of 1 time period,
t be the number of time periods,
p be the payment each time period.
As the first payment is being taken immediately:
sa^n = p(a^n + a^(n – 1) + … + a^2 + a)
= pa(a^n – 1) / (a – 1)
s = p(a^n – 1) / (a – 1)a^(n – 1)
a = 1.03 (3% per half-year)
n = 10 (number of half-years)
p = $4000
s = $4000(1.03^10 – 1) / (0.03 * 1.03^9)
= $35144.44.