man pays a premium of $ 100 at the beginning of every year to an insurance company the understand that at the end of 15 years he can receive the premiums he has paid with 5% compound interest. Much?

To calculate the amount the man will receive at the end of 15 years with a 5% compound interest, we can use the formula for the future value of an ordinary annuity:

FV = P * ((1 + r)^n - 1) / r

Where:
FV = Future Value
P = Annual payment (premium)
r = Interest rate per period (5% or 0.05)
n = Number of periods (15 years)

Plugging in the values, we get:

FV = 100 * ((1 + 0.05)^15 - 1) / 0.05
FV = 100 * (1.05^15 - 1) / 0.05
FV ≈ 100 * (1.971 - 1) / 0.05
FV ≈ 100 * 0.971 / 0.05
FV ≈ 1942

Therefore, the man will receive approximately $1,942 at the end of 15 years with a 5% compound interest.