Mr. and Mrs.Eng's property taxes,accounting to $2450, are due on July 1. What amount should the City accept if the taxes are paid 8 months in advance and the City can earn 6% compounded monthly on surplus funds?
To determine the amount that should be paid to the City if the taxes are paid 8 months in advance, we need to calculate the present value of $2450.
We know that the City can earn 6% compounded monthly on surplus funds. This means that the interest is compounded 12 times a year. To calculate the present value, we can use the formula for the present value of a future value:
Present Value = Future Value / (1 + interest rate)^n
Where:
- Future Value is the amount to be paid ($2450)
- Interest rate is the monthly interest rate (6% / 12 = 0.005)
- n is the number of compounding periods (8)
Plugging in the values, we get:
Present Value = $2450 / (1 + 0.005)^8
Calculating the present value using a calculator or spreadsheet, we find that the amount Mr. and Mrs. Eng should pay to the City is approximately $2298.11.
Therefore, the City should accept approximately $2298.11 if the taxes are paid 8 months in advance.