Question

An insurance settlement of 1.5 million must replace Trixie Edens income for the next 30 years. What income will the settlement provide at the end of each month if it is invested at an annuity that earns 7.9% compounded monthly solve the problem round your answer to the nearest cent 

Answer 1

the insurance settlement will provide approximately $634,180.60 at the end of each month if it is invested in an annuity that earns 7.9% compounded monthly.

Explanation:

To calculate the income provided by the insurance settlement at the end of each month, we can use the formula for the future value of an ordinary annuity:

Future Value (FV) = P * [(1 + r/n)^(nt) - 1] / (r/n)

Where:

P = Principal amount (insurance settlement)

r = Annual interest rate (expressed as a decimal)

n = Number of times interest is compounded per year (monthly compounding means n = 12)

t = Number of years (30 years)

Given values:

P = $1,500,000

r = 7.9% = 0.079 (as a decimal)

n = 12 (monthly compounding)

t = 30 years

Now, let's calculate the future value (monthly income):

FV = $1,500,000 * [(1 + 0.079/12)^(12*30) - 1] / (0.079/12)

FV ≈ $1,500,000 * [(1.0065833333333333)^(360) - 1] / (0.0065833333333333)

FV ≈ $1,500,000 * [2.785464346872476] / 0.0065833333333333

FV ≈ $634,180.60

So, the insurance settlement will provide approximately $634,180.60 at the end of each month if it is invested in an annuity that earns 7.9% compounded monthly.