A life insurer receives $500,000 in premiums and invests them at an interest rate of 3.5% per annum. Calculate the accumulated value after 2 years (to 2 decimal places).
answer: 535612.50
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To calculate the accumulated value after 2 years, we need to use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = Accumulated value
P = Principal amount (premiums received)
r = Interest rate per period
n = Number of compounding periods per year
t = Number of years
Given:
P = $500,000
r = 3.5% per annum (or 0.035 as a decimal)
n = 1 (compounded annually)
t = 2 years
Substituting these values into the formula:
A = 500,000(1 + 0.035/1)^(1*2)
A = 500,000(1.035)^2
A = 500,000(1.071225)
A ≈ $535,612.50
Therefore, the accumulated value after 2 years is approximately $535,612.50.
To calculate the accumulated value, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = Accumulated value
P = Principal amount (premiums)
r = Annual interest rate (as a decimal)
n = Number of times interest is compounded per year
t = Number of years
In this case, the principal amount (P) is $500,000, the annual interest rate (r) is 3.5% (or 0.035 as a decimal), the number of times interest is compounded per year (n) is usually not given, so we'll assume it is compounded annually (n = 1), and the number of years (t) is 2.
Substituting these values into the formula, we get:
A = 500,000(1 + 0.035/1)^(1*2)
A = 500,000(1 + 0.035)^2
A = 500,000(1.035)^2
A ≈ 500,000(1.071225)
A ≈ 535,612.50
Therefore, the accumulated value after 2 years will be approximately $535,612.50.