if a regular payment is made quarterly into sinking fund,it accrues to $18258.53 after ten years.What is the annual percentage rate paid by the fund?

To find the annual percentage rate (APR) paid by the sinking fund, we can use the concept of compound interest.

First, let's break down the information given in the problem:

- The regular payment is made quarterly, meaning four times a year.
- The fund accrues to $18,258.53 after ten years.

To calculate the APR, we need to determine the interest rate (r) per quarter and then convert it to an annual rate.

Let's go step by step:

1. Calculate the quarterly interest rate:
We can use the formula for compound interest: A = P(1 + r/n)^(n*t), where:
- A is the future value of the sinking fund ($18,258.53 in this case).
- P is the regular payment.
- r is the quarterly interest rate.
- n is the number of times interest is compounded per year (4 for quarterly).

In this case, we are solving for r. Plugging in the given values, we get:
$18,258.53 = P(1 + r/4)^(4*10)

2. Solve for r:
To isolate r, we need to manipulate the equation. First, divide both sides of the equation by P:
($18,258.53 / P) = (1 + r/4)^(4*10)

Next, we can take the 10th root of both sides:
(1 + r/4) = (18,258.53 / P)^(1/(4*10))

3. Calculate the quarterly interest rate:
Subtract 1 from both sides:
r/4 = (18,258.53 / P)^(1/(4*10)) - 1

Multiply both sides by 4 to get the quarterly interest rate:
r = 4 * ((18,258.53 / P)^(1/(4*10)) - 1)

4. Convert the quarterly rate to an annual percentage rate:
To convert the quarterly rate to an annual rate, we multiply by 4 (since there are four quarters in a year).

Hence, the APR paid by the sinking fund is given by:
APR = 4 * r

To find the exact APR, you will need to know the value of the regular payment (P) made into the sinking fund.