Question

Annuity vs. Lump Sum

At what interest rate (as an EAR) would you be indifferent between the following two choices: 1) receiving $10,000 per year, starting 1 year from today, for a total of 2 payments (the last payment occurs 2 years from today in that case)... OR, 2) receiving $20,679 exactly 2 years from today? Answer: _____%  

Margin of error for correct responses: +/- .03%.

Answer 1

To remain indifferent in both the option,

Future Value in Option 1 = Future Value in Option 2

Future value of Payment 1 + Future value of payment 2 = 20769

10000 * ( 1 + r ) + 10,000 = 20,769

10000 * ( 1 + r ) = 10,769

( 1 + r ) = 10,769 / 10000

r = 1.0769 - 1

r = 0.0769 or 7.69 % Answer