Question 1
Multiple ChoiceA financial planner receives a three-year consulting contract with the following end-of-year payments:
1 | $80,000 |
|---|---|
2 | $120,000 |
3 | $180,000 |
She expects to invest these payments at an annual interest rate of 4%, compounded annually, until her retirement 10 years from now. The value of these amounts at the end of 10 years is closest to:
Explanation
We must calculate the future value of each individual payment, compounding it forward to Year 10:
FV of Year 1 payment ($80,000):
FV = 80,000 × (1.04)^9 = 80,000 × 1.432 = $114,560FV of Year 2 payment ($120,000):
FV = 120,000 × (1.04)^8 = 120,000 × 1.3686 = $164,232FV of Year 3 payment ($180,000):
FV = 180,000 × (1.04)^7 = 180,000 × 1.319 = $237,078
Total Future Value ≈ $114,560 + $164,232 + $237,078 = $544,370
BA II Plus Steps:
You’ll do three individual FV calculations:
1. For Year 1:
N = 9
I/Y = 4
PV = -80,000
PMT = 0
CPT → FV = 114,560
2. For Year 2:
N = 8
PV = -120,000
CPT → FV = 164,232
3. For Year 3:
N = 7
PV = -180,000
CPT → FV = 237,078
Then manually add the three results to get: $544,370.
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