a Woman insures ber life at 3 million naira by paying a premium of 2,000 Nair for 20 years.After 20 years the insurance company ends the agreement and gives her 50,000 naira of compound interest at 8 percent.Find the actual value of premiums paid and the profit made by the company
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Well, it seems like this woman had quite the "premium" deal! Let's calculate the actual value of premiums paid and the profit made by the company, shall we?
First, let's find the total amount of premiums paid over 20 years. The woman paid a premium of 2,000 Naira each year for 20 years, so the total amount of premiums paid is:
2,000 Naira × 20 years = 40,000 Naira
Now, let's calculate the compound interest earned by the woman over 20 years. The insurance company gave her 50,000 Naira as compound interest at 8 percent, so the principal amount (P) can be calculated using the compound interest formula:
P = A / (1 + r/n)^(nt)
Where:
A = 50,000 Naira (the compound interest amount)
r = 8% (annual interest rate in decimal form, so 0.08)
t = 20 years (time in years)
n = 1 (since the interest is compounded annually)
P = 50,000 / (1 + 0.08/1)^(1 * 20)
P = 50,000 / (1.08)^20
P ≈ 17,889.64 Naira
Now, let's find the actual value of premiums paid by subtracting the compound interest from the total premiums:
Actual value of premiums paid = Total premiums paid - Compound interest received
Actual value of premiums paid = 40,000 - 17,889.64
Actual value of premiums paid ≈ 22,110.36 Naira
Finally, let's calculate the profit made by the insurance company by subtracting the actual value of premiums paid from the compound interest received:
Profit made by the company = Compound interest received - Actual value of premiums paid
Profit made by the company = 17,889.64 - 22,110.36
Profit made by the company ≈ -4,220.72 Naira
Uh-oh! It seems like the insurance company incurred a loss of approximately 4,220.72 Naira. I guess this time the jokes on them!
To find the actual value of premiums paid and the profit made by the company, we need to calculate the total amount of premiums paid over 20 years and the compound interest earned by the insurance company on those premiums.
First, let's calculate the total amount of premiums paid over 20 years:
Premium per year = 2,000 Naira
Total number of years = 20 years
Total premiums paid = Premium per year x Total number of years = 2,000 Naira/year x 20 years = 40,000 Naira
Next, let's calculate the compound interest earned by the insurance company on those premiums:
Principal amount (amount insured) = 3,000,000 Naira
Interest rate = 8%
Compound interest = Principal amount x (1 + Interest rate/100) ^ Total number of years - Principal amount
Compound interest = 3,000,000 Naira x (1 + 8/100) ^ 20 - 3,000,000 Naira
Now, let's calculate the profit made by the company:
Profit = Compound interest - Total premiums paid
Profit = (3,000,000 Naira x (1 + 8/100) ^ 20 - 3,000,000 Naira) - 40,000 Naira
Simplifying the equation will give us the profit made by the company.
Please note that the exact calculation may vary depending on the specific terms and conditions of the insurance policy.
To find the actual value of the premiums paid by the woman, we need to calculate the total amount she paid over the 20-year period. The premium amount is given as 2,000 Naira.
Total amount paid = premium amount * number of years
= 2,000 Naira * 20 years
= 40,000 Naira
Therefore, the actual value of premiums paid by the woman is 40,000 Naira.
Next, let's calculate the compound interest provided by the insurance company after 20 years. The interest rate is given as 8 percent.
Compound interest formula:
A = P * (1 + r/n)^(n*t)
Where:
A = Final amount
P = Principal amount (initial investment)
r = Annual interest rate (as a decimal)
n = Number of times that interest is compounded per year
t = Number of years
In this case:
Principal amount (P) = 3,000,000 Naira
Annual interest rate (r) = 8% or 0.08 (expressed as a decimal)
Number of times interest is compounded per year (n) = 1
Number of years (t) = 20
A = 3,000,000 Naira * (1 + 0.08/1)^(1*20)
A = 3,000,000 Naira * (1 + 0.08)^20
A = 3,000,000 Naira * (1.08)^20
A ≈ 3,000,000 Naira * 4.661648
A ≈ 13,984,943.82 Naira
So, after 20 years, the insurance company gives the woman approximately 13,984,943.82 Naira.
To calculate the profit made by the insurance company, subtract the total amount paid from the final amount provided by the insurance company:
Profit = Final amount - Total amount paid
= 13,984,943.82 Naira - 40,000 Naira
≈ 13,944,943.82 Naira
Therefore, the profit made by the insurance company is approximately 13,944,943.82 Naira.