Final answer:
To accumulate $9000 in three years with a 7% monthly compounded interest, approximately $7,981.25 should be deposited today.
Step-by-step explanation:
To calculate the amount of money that should be deposited today to accumulate $9000 in three years with a 7% monthly compounded interest, we can use the formula:
A = P(1 + r/n)^(nt)
where A is the future value, P is the principal (the amount to be deposited today), r is the annual interest rate (converted to a decimal), n is the number of times interest is compounded per year, and t is the number of years. In this case, the future value A is $9000, the annual interest rate r is 7%/12 (converted to a monthly rate), n is 12 (compounded monthly), and t is 3 years. Plugging these values into the formula, we get:
9000 = P(1 + (0.07/12))^(12*3)
Simplifying the equation, we find:
P = 9000 / (1 + (0.07/12))^(12*3)
Calculating this expression, the value of P is approximately $7,981.25. Therefore, the correct answer is option B) $7,981.25.