Question

What is the current economic value of an inheritance that will pay $1800 to the beneficiary at the beginning of every three months for 25 years, starting when the beneficiary reaches 20 years of age, 312312 years from now? Assume that money is worth 7.9% compounded monthly. (Do not round intermediate calculations and round your final answer to the nearest dollar.)

  

Today's value

$

Answer 1

Monthly Rate = 0.079/12 = 0.006583

Effective Quarterly Rate = [(1+0.006583)^3]-1 = 0.01988

PV of Perpetual Annuity when beneficiary reaches 20 years i.e. 312312 years from now = PV of Perpetual Annuity + Annuity amount(1 Additional Installment because it is paid at BEGINNING of every Quarter)

= [Annuity Amount/Effectively Quarterly Rate]+Annuity Amount

= [1800/0.01988]+1800

= 90541.87+1800

= 92341.87

PV of 92341.87 TODAY = Future Value/[(1+Monthly Interest Rate)^Number of Months]

= 92341.87/[(1+0.006583)^(312312*12)]

Note: It is NOT POSSIBLE TO FURTHER CALCULATE, because the Denominator will be Infinity.

Therefore, We can conclude Final Answer as $0.01, so rounding it to nearest Dollar can be $0 or $1(in case, a nominal amount is to be considered).