Questions: Find the amount (future value) of an ordinary annuity of 12 monthly payments at 150 each that earn interest at 10% per year compounded monthly

Find the amount (future value) of an ordinary annuity of 12 monthly payments at 150 each that earn interest at 10% per year compounded monthly

Transcript text: 6) Find the amount (future value) of an ordinary annuity of 12 monthly payments at $\$ 150$ each that earn interest at 10\% per year compounded monthly

Solution

Solution Steps

To find the future value of an ordinary annuity, we use the future value of an annuity formula. This formula takes into account the regular payment amount, the interest rate per period, and the total number of payments. The formula is:

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

where:

$ FV $ is the future value of the annuity.
$ P $ is the payment amount per period.
$ r $ is the interest rate per period.
$ n $ is the total number of payments.

In this case, the payment amount $ P $ is $150, the annual interest rate is 10%, which needs to be converted to a monthly rate, and the number of payments $ n $ is 12.

Step 1: Identify Given Values

We are given the following values for the ordinary annuity:

$ P = 150 $ (monthly payment)
Annual interest rate $ = 0.10 $
Total number of payments $ n = 12 $

Step 2: Convert Annual Interest Rate to Monthly Rate

The monthly interest rate $ r $ is calculated as: \[ r = \frac{0.10}{12} = 0.0083333333 \]

Step 3: Apply the Future Value of Annuity Formula

The future value $ FV $ of the annuity can be calculated using the formula: \[ FV = P \times \frac{(1 + r)^n - 1}{r} \] Substituting the known values: \[ FV = 150 \times \frac{(1 + 0.0083333333)^{12} - 1}{0.0083333333} \]

Step 4: Calculate Future Value

After performing the calculations, we find: \[ FV \approx 1884.8352 \]