Question

The Clark family wants to save money to travel the world. They plan to invest in an ordinary annuity that earns 7.8% interest, compounded monthly. Payments will be made at the end of each month. How much money do they need to pay into the annuity each month for the annuity to have a total value of $12,000 after 10 years? Do not round intermediate computations, and round your final answer to the nearest cent. If necessary, refer to the list of financial formulas.

Answer 1

To have a total value of $12,000 after 10 years, the Clark family needs to pay approximately $74.12 into the annuity each month.

Step-by-step explanation:

To calculate the amount of money the Clark family needs to pay into the annuity each month, we can use the formula for the future value of an ordinary annuity:

`FV = P × [(1 + r/n)^(n × t) - 1] / (r/n)`

Where:
FV is the future value (in this case, $12,000)
P is the monthly payment
r is the annual interest rate (7.8%)
n is the number of compounding periods per year (12)
t is the number of years (10)

Plugging in the values, we get:

`$12,000 = P × [(1 + 0.078/12)^(12 × 10) - 1] / (0.078/12)`

Solving this equation, we find that the Clark family needs to pay approximately $74.12 into the annuity each month to have a total value of $12,000 after 10 years.