Answer:
To calculate the amount you would need to deposit in an account with a 6% interest rate, compounded quarterly, to have $2250 in your account 17 years later, we can use the formula for compound interest:
�
=
�
(
1
+
�
�
)
�
�
A=P(1+nr)nt
where:
A is the amount of money in the account after t years.
P is the principal amount (the initial amount of money deposited).
r is the annual interest rate (as a decimal).
n is the number of times the interest is compounded per year.
t is the number of years.
In this case, we know that:
A = $2250
r = 6% = 0.06
n = 4 (since the interest is compounded quarterly)
t = 17 years
Substituting these values into the formula, we get:
2250
=
�
(
1
+
0.06
4
)
(
4
)
(
17
)
2250=P(1+40.06)(4)(17)
Simplifying the right-hand side of the equation, we get:
2250
=
�
(
1.015
)
68
2250=P(1.015)68
Dividing both sides by
(
1.015
)
68
(1.015)68, we get:
�
=
2250
(
1.015
)
68
≈
734.34
Step-by-step explanation:
Therefore, you would need to deposit $734.34 into the account to have $2250 in your account 17 years later, rounded to the nearest cent.
