Asked by Logan Tippett on May 03, 2024
Verified
You are considering two insurance settlement offers. The first offer includes annual payments of $5,000, $7,500, and $10,000 over the next three years, respectively. The other offer is the payment of one lump sum amount today. You are trying to decide which offer to accept given the fact that your discount rate is 5%. What is the minimum amount that you will accept today if you are to select the lump sum offer?
A) $19,877.67
B) $20,203.00
C) $21,213.15
D) $23,387.50
E) $24,556.88
Insurance Settlement
The payment made by an insurance company to a policyholder or claimant as compensation for a covered loss.
Discount Rate
in finance, refers to the interest rate used in discounted cash flow (DCF) analysis to determine the present value of future cash flows.
Lump Sum
A single payment made at a particular time, as opposed to multiple payments over time.
- Gain an understanding of the present value concept and the steps involved in its calculation.
- Analyze potential investments by determining their present worth.
Verified Answer
TM
Trixie MendezMay 09, 2024
Final Answer :
B
Explanation :
We can calculate the present value of the three annual payments using the formula:
PV = PMT1 / (1 + r) + PMT2 / (1 + r)² + PMT3 / (1 + r)³
where PV is the present value, PMT is the payment in a year, and r is the discount rate.
Substituting the values, we get:
PV = 5,000 / (1 + 0.05) + 7,500 / (1 + 0.05)² + 10,000 / (1 + 0.05)³
PV = $20,203.00
Therefore, the lump sum offer should be at least $20,203.00 to be equivalent to the three annual payments. The answer is B.
PV = PMT1 / (1 + r) + PMT2 / (1 + r)² + PMT3 / (1 + r)³
where PV is the present value, PMT is the payment in a year, and r is the discount rate.
Substituting the values, we get:
PV = 5,000 / (1 + 0.05) + 7,500 / (1 + 0.05)² + 10,000 / (1 + 0.05)³
PV = $20,203.00
Therefore, the lump sum offer should be at least $20,203.00 to be equivalent to the three annual payments. The answer is B.
Learning Objectives
- Gain an understanding of the present value concept and the steps involved in its calculation.
- Analyze potential investments by determining their present worth.