Question 1198081: The following table shows the average life expectancies in several countries. Assume that all premiums you calculate are based on end-of-month deposits in a fund yielding 6.8% annual interest compounded monthly to be paid out when a person reaches the life expectancy. HINT [See Example 2.]
Country Japan Canada U.K. U.S. Mexico China India
Life
Expectancy:
Male 80 80 79 76 73 74 64
Life
Expectancy:
Female 87 84 83 81 79 77 68
Calculate the life insurance monthly premium that a 50-year-old female in Japan would pay for a $10,000,000 policy. (Round your answer to the nearest cent.)
Answer by onyulee(41)   (Show Source):
You can put this solution on YOUR website! **1. Determine the Number of Months**
* Life expectancy for a 50-year-old female in Japan: 87 years
* Years to live: 87 years - 50 years = 37 years
* Number of months to live: 37 years * 12 months/year = 444 months
**2. Calculate the Monthly Interest Rate**
* Annual interest rate: 6.8%
* Monthly interest rate: 6.8% / 12 = 0.5667%
**3. Calculate the Future Value of a Single Deposit**
* We need to find the future value of a single deposit that will grow to $10,000,000 in 444 months.
* Use the future value of an ordinary annuity formula:
* FV = P * [(1 + r)^n - 1] / r
* Where:
* FV = Future Value ($10,000,000)
* P = Monthly Premium (unknown)
* r = Monthly interest rate (0.005667)
* n = Number of months (444)
**4. Solve for the Monthly Premium (P)**
* Rearrange the formula to solve for P:
* P = FV * [r / ((1 + r)^n - 1)]
* Substitute the values:
* P = $10,000,000 * [0.005667 / ((1 + 0.005667)^444 - 1)]
* Calculate P:
* P ≈ $10,000,000 * [0.005667 / (15.236 - 1)]
* P ≈ $10,000,000 * [0.005667 / 14.236]
* P ≈ $10,000,000 * 0.000398
* P ≈ $3,980
**Therefore, the monthly premium for a 50-year-old female in Japan for a $10,000,000 life insurance policy would be approximately $3,980.**
**Note:**
* This calculation assumes that the interest rate remains constant over the entire 37-year period, which may not be the case in reality.
* This calculation also assumes that the individual lives exactly to the life expectancy.
* This is a simplified model and actual life insurance premiums are determined by various factors, including health, lifestyle, and other risk factors.
This information is for illustrative purposes only and does not constitute financial advice. Please consult with a qualified financial advisor for personalized guidance.
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