Question

You are managing a trust fund that must pay its owner $17,756 each month, for 86 months, (starting next month). How much do you need to invest today to make the trust fund payments if your investments earn 4.05% APR (compounded monthly)?

Answer 1

Given,

Monthly Payments owner gets from the funds = MP = $17756

Annual Percentage Rate = APR = r = 4.05% = 0.0405

number of payments per year = m = 12

Present Value of investment = P = ?

and

n = total number of months = 86 months

Substituting these values in the following equation, we get

MP = P * (r/m)/ (1-(1+(r/m))^-n)

Rearraging the equation for value P, we get

P = MP* (1-(1+(r/m))^-n)/ (r/m)

P = 17756 * (1-(1+(0.0405/12)^-86)/ (0.0405/12)

P = 17756* (1-(1+0.0034)^-86)/ (0.0034)

P = 17756* (1-(1.0034)^-86)/ 0.0034

P = 17756*(1-0.7484)/ 0.0034

P = (17756*0.2516)/ 0.0034

P = 4466.66/ 0.0034

P = 1313724

Therefore, we need to invest $13,13,724 today in trust fund.