Question

true or false, you are self-employed and your income is not spread out evenly over the year. you just finished a large job that leaves net income of 250000. the annual interest rate is 6.5%.this amount is sufficient to pay yourself at least 5000 per month for the next 60 months.

Answer 1

false.

we need to find out the present value of 5000 per month payment for 60 months discounted @6.5% per annum.

if this amount is greater than 250,000 then the answer is false, else true.

present value of annuity payments = P*[1 - (1 + r)^(-n)] /r

here,

P = 5,000

r = 6.5% per annum => 6.5 / 12 =>0.541667%

=>0.00541667

n = 60 months

now,

present value of payments =5,000*[1 -(1.00541667)^(-60)] / 0.00541667

=>5,000*[0.2768388/0.00541667]

=>5000*51.1086701

=>$255,543.35.

since the present value of the given stream of payments is greater than $250,000, the amount is not sufficient to pay 5,000 per month for next 60 months when interest rate is 6.5%.