Asked by Nicholas Jacobs on Jul 05, 2024
Verified
You just won the lottery,and you have a choice between receiving $3,500,000 today or a 10-year annuity of $500,000,with the first payment coming 1 year from today.What rate of return is built into the annuity?
A) 6.72%
B) 7.07%
C) 7.43%
D) 7.80%
Annuity
A financial product that pays out a fixed stream of payments to an individual, typically used as part of retirement strategy.
Lottery
A form of gambling or a game of chance where participants buy tickets for a chance to win prizes, often financial in nature.
Return
The gain or loss on an investment over a specific period, represented as a percentage of the investment’s cost.
- Assess the efficiency of interest rates based on various compounding periods to determine the most advantageous investment choice.
Verified Answer
YG
Yulianna GarciaJul 11, 2024
Final Answer :
B
Explanation :
To calculate the rate of return built into the annuity, we can use the present value formula for an annuity:
PV = PMT * (1 - 1/(1+r)^n) / r
where PV is the present value of the annuity ($3,500,000 in this case), PMT is the payment per period ($500,000), r is the rate of return per period, and n is the number of periods (10 years).
Plugging in the numbers and solving for r gives:
$3,500,000 = $500,000 * (1 - 1/(1+r)^10) / r
r = 7.07%
Therefore, the best choice is to take the annuity, as the rate of return (7.07%) is higher than what could be earned through a low-risk investment like a savings account.
PV = PMT * (1 - 1/(1+r)^n) / r
where PV is the present value of the annuity ($3,500,000 in this case), PMT is the payment per period ($500,000), r is the rate of return per period, and n is the number of periods (10 years).
Plugging in the numbers and solving for r gives:
$3,500,000 = $500,000 * (1 - 1/(1+r)^10) / r
r = 7.07%
Therefore, the best choice is to take the annuity, as the rate of return (7.07%) is higher than what could be earned through a low-risk investment like a savings account.
Learning Objectives
- Assess the efficiency of interest rates based on various compounding periods to determine the most advantageous investment choice.