A year-end bonus of $24,000 will generate how much money at the beginning of each month for the next year, if it can be invested at 6.45%, compounded monthly? (Round your answer to the nearest cent.)
A year-end bonus of $24,000 will generate how much money at the beginning of each month for the next year, if it can be invested at 6.45%, compounded monthly? (Round your answer to the nearest cent.)
To find out how much money the year-end bonus will generate at the beginning of each month for the next year, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount (including the principal)
P = the principal amount (initial investment)
r = the annual interest rate (in decimal form)
n = the number of times interest is compounded per year
t = the number of years
Given:
Principal (P) = $24,000
Annual interest rate (r) = 6.45% = 0.0645 (in decimal form)
Compounding frequency (n) = 12 (monthly)
Number of years (t) = 1
Applying these values to the formula, we get:
A = 24000(1 + 0.0645/12)^(12*1)
Simplifying:
A = 24000(1.005375)^12
Using a calculator, we can evaluate the exponent:
A ≈ 24000(1.0664071)
A ≈ $25,593.77
Therefore, the year-end bonus of $24,000 will generate approximately $25,593.77 at the beginning of each month for the next year, when invested at a 6.45% interest rate compounded monthly.