Final answer:
To obtain $8,700 in 9 years at an interest rate of 2% per year compounded quarterly, approximately $6,772.09 needs to be deposited now into the account.
Step-by-step explanation:
To find out how much money needs to be deposited now into an account to obtain $8,700 in 9 years with an interest rate of 2% per year compounded quarterly, you can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
- A is the future value ($8,700 in this case)
- P is the principal amount (the amount to be deposited now, which we need to find)
- r is the annual interest rate (2% per year in this case)
- n is the number of times the interest is compounded per year (4 times per year in this case)
- t is the number of years (9 years in this case)
Plugging in the given values into the formula, we get:
8,700 = P(1 + 0.02/4)^(4*9)
Simplifying the equation, we can then solve for P:
P = 8,700 / (1 + 0.02/4)^(4*9)
P = 8,700 / (1 + 0.005)^(36)
Calculating this on a calculator, the principal amount (P) comes out to be approximately $6,772.09. Therefore, approximately $6,772.09 needs to be deposited now into the account to obtain $8,700 in 9 years.