Question

Megan wants to retire in 20 years, and she wants to have an annuity of $50,000 a year for 25 years after retirement. Megan wants to receive the first annuity payment the day she retires. Using an interest rate of 8%, the amount that Megan must invest today in order to have her retirement annuity is closest to:

		$123,670
		$204,850
		$377,910
		$576,440

Answer 1

Answer is $123,670

After retirement:

Annual payment = $50,000
Number of payments = 25
Interest rate = 8%

Amount required at retirement = $50,000 + $50,000/1.08 + … + $50,000/1.08^23 + $50,000/1.08^24
Amount required at retirement = $50,000 * 1.08 * (1 - (1/1.08)^25) / 0.08
Amount required at retirement = $50,000 * 11.528758
Amount required at retirement = $576,437.90

Before retirement:

Time period = 20 years

Amount invested = $576,437.90/1.08^20
Amount invested = $123,670

Therefore, Megan must invest $123,670 today in order to have her retirement annuity.