Final answer:
The question relates to solving for the number of periods (n) in an ordinary annuity given the future value, periodic payment, and annual interest rate using the future value of an ordinary annuity formula. It involves dividing the annual interest rate by 12 to find the monthly rate and then using logarithms to rearrange the formula and solve for n.
Step-by-step explanation:
The student is asking for help using the future value of an ordinary annuity formula to find the number of periods (n) for given values of the future value (a), periodic payment (R), and annual interest rate (r). The formula for the future value of an ordinary annuity is:
FV = R * [((1 + i)^n - 1) / i]
Where:
- FV is the future value of the annuity
- R is the periodic payment
- i is the periodic interest rate (annual interest rate divided by the number of periods per year)
- n is the total number of payments or periods
In the provided question, we know:
- FV (Future Value) = $19,500
- R (Monthly Payment) = $200
- Annual interest rate r = 9.5%
The student should divide the annual interest rate by 12 to find the monthly interest rate and then use the formula for the future value of an ordinary annuity to find the number of periods (n). This requires rearranging the formula to solve for n, which involves logarithms. As the provided information is insufficient to calculate n directly (the setup of the equation is not fully provided), it would be necessary for the student to first understand how to correctly set up the equation before solving for n.