Question

12. What is the current economic value of an inheritance that will pay $2000 to the beneficiary at the beginning of every 3 months for 20 years, starting when the beneficiary reaches 20 years of age, 4½ years from now? Assume that money is worth 9% compounded monthly.

Answer 1

Annual interest rate = 9.00%
Monthly interest rate = 9.00% / 12
Monthly interest rate = 0.75%

Effective annual rate = (1 + Monthly interest rate)^12 - 1
Effective annual rate = (1 + 0.0075)^12 - 1
Effective annual rate = 1.093807 - 1
Effective annual rate = 0.093807 or 9.3807%

Quarterly interest rate = (1 + Effective annual rate)^(1/4) - 1
Quarterly interest rate = (1 + 0.093807)^(1/4) - 1
Quarterly interest rate = 1.02267 - 1
Quarterly interest rate = 0.02267 or 2.267%

Quarterly payment = $2,000
Time period = 20 years or 80 quarters

First payment is made after 4.50 years or 18 quarters

Present value = $2,000/1.02267^18 + $2,000/1.02267^19 + … + $2,000/1.02267^96 + $2,000/1.02267^97
Present value = $2,000 * (1/1.02267)^17 * (1 - (1/1.02267)^80) / 0.02267
Present value = $2,000 * 25.118942
Present value = $50,237.88

Therefore, current economic value of inheritance is $50,237.88