Question

Tim Crowe has a trust fund that will be worth $75,000 on his 18th birthday. Starting then, he will recieve equal monthly payments at the beginning of each month for five years. The trust fund is expected to earn 9% compounded monthly over the five years. How much will Tim recieve each month?

Answer 1

This can be solved usinf formula of present value of annuity due

here PV = 75000$,

n = no of payments = 5 x 12 =60

r = 9%/12 =0.75%

PV(annuity due) = Monthly Receipt x [1-(1/(1+r)^n / r ] x (1+r)

75000 =  Monthly Receipt x [1-(1/(1+0.75%)^60 / 0.75%] x (1+0.75%)

75000 = Monthly Receipt x [1-(1/(1+0.0075)^60 / 0.0075] x (1+0.0075)

75000 = Monthly Receipt x [1-(1/(1.0075)^60 / 0.0075] x (1.0075)

75000 = Monthly Receipt x [1-0.6387 / 0.0075] x (1.0075)

75000 = Monthly Receipt x 0.3613/0.0075 x 1.0075

75000 = Monthly Receipt x 48.1734 x 1.0075

75000 = Monthly Receipt x 48.5347

Monthly Receipt = 1545.29 $

Thus tim will receive $1545.29 per month