Question

What is the current economic value of an inheritance that will pay $2700 to the beneficiary at the beginning of every three months for 20 years, starting when the beneficiary reaches 20 years of age, 4 and a half years from now? Assume that money is worth 6.7% compounded monthly. (Do not round intermediate calculations and round your final answer to the nearest dollar.)

  

Today's value

$

Answer 1

We have int rate 6.7% compunded monthly we need to find out the int rate compounded quarterly as the payments are quarterly

( 1 + i)^4 = (1+0.067/12)^12

i = 1.68% for 3 months

present value of annuity due = annuity + annuity * [ 1 - ( 1+i)^-(n-1) ] / i

= 2700 + 2700* [ 1 - 1.0168^-20*4] /0.0168

= 121029.40

we have 121029.40 at age 20 .

Todays value = 121029.40 / ( 1 + i)^no of periods

= 121029.40/1.0168^2.5*4

= 102455.50