Betty and Bob buy a membership on the WORLDEX, costing

$650,000, by making payments to the bank at the end of June and at the end of December for 11 years. What should these equal payments be? Your final answer should be correct to 2 places after the decimal point.interest rates are 12% per annum compounded semiannually.

To calculate the equal payments Betty and Bob should make, we will use the formula for the **present value of an ordinary annuity**, as the payments are made at the end of each period (June and December).

The formula for the present value of an ordinary annuity is:

\[
PV = P \times \left(1 - (1 + i)^{-n} \right) / i
\]

Where:
- $ PV $ is the present value (in this case, $650,000)
- $ P $ is the periodic payment (what we're solving for)
- $ i $ is the interest rate per period
- $ n $ is the total number of payments

### Step 1: Determine the interest rate per period
The annual interest rate is 12%, compounded semiannually. So, the interest rate per period (every six months) is:

\[
i = \frac{12\%}{2} = 6\% = 0.06
\]

### Step 2: Determine the number of payments
The payments are made semiannually for 11 years. So, the total number of payments is:

\[
n = 11 \times 2 = 22 \text{ payments}
\]

### Step 3: Rearrange the formula to solve for $ P $
Now, we rearrange the formula to solve for $ P $:

\[
P = \frac{PV \times i}{1 - (1 + i)^{-n}}
\]

Substituting the known values:

\[
P = \frac{650,000 \times 0.06}{1 - (1 + 0.06)^{-22}}
\]

### Step 4: Solve for $ P $
I'll now calculate the value.The equal semiannual payments that Betty and Bob should make are approximately **$53,979.62**.

Would you like further details on the calculation or have any other questions? 

Here are 5 related questions you might find interesting:
1. How would the payment change if the interest rate were compounded quarterly?
2. What if the payments were made annually instead of semiannually?
3. How much total interest will Betty and Bob pay over the 11 years?
4. What happens to the payment amount if the loan term is extended to 15 years?
5. Can we calculate the future value of these payments?

**Tip:** When dealing with annuities, always ensure you adjust the interest rate and number of periods to match the compounding frequency.

Betty and Bob buy a membership on the WORLDEX, costing $650,000, by making payments to the bank at the end of June and at the end of December for 11 years. What should these equal payments be? Your final answer should be correct to 2 places after the decimal point. Interest rates are 12% per annum compounded semiannually.

Learn how to calculate equal semiannual payments for a $650,000 membership over 11 years with a 12% interest rate compounded semiannually. This step-by-step solution explains the present value of an annuity formula and guides you through solving for equal payments, rounding to two decimal places.

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