Calculate Annual Interest Rate

A

On the BAII Plus, press 10 N, 0 PV, 500 PMT, 9000 +/- FV, CPT I/Y. On the HP12C, press 10 n, 0 PV, 500 PMT, 9000 CHS FV, i. Make sure the BAII Plus has the

P/Y value set to 1.

To solve this question, we need to find the annual interest rate that would cause a series of 10 deposits of $500 each to accumulate to a total of $9,000, assuming the first deposit is made one year from today.

Let's break down the problem step by step:

1. We know that the deposits are made annually and the first deposit is made one year from today. This means we have a timeline of 10 years for the deposits to accumulate.

2. The future value of an ordinary annuity formula can be used to calculate the total accumulation. The formula is:

   FV = P * [(1 + r)^n - 1] / r

   where: FV = Future value (desired accumulation) P = Payment (deposit amount) r = Annual interest rate n = Number of periods (number of deposits)

   In this case, FV = $9,000, P = $500, and n = 10. We need to solve for r.

3. Rearranging the formula to solve for r, we get:

   r = [(FV / P)^(1/n) - 1]

   Plugging in the values, we have:

   r = [($9,000 / $500)^(1/10) - 1]

4. Calculating the expression inside the brackets first:

   ($9,000 / $500)^(1/10) ≈ 1.183215956

   Subtracting 1 from the result:

   1.183215956 - 1 ≈ 0.183215956

5. Multiplying the result by 100 to convert it to a percentage:

   0.183215956 * 100 ≈ 18.32%