Final answer:
The question is about calculating the future value of a series of monthly deposits into an account with compound interest. Using the values provided, you use the future value formula of an ordinary annuity to determine the final amount after the last deposit made by Shirley on 30 September 2019.
Step-by-step explanation:
The student is asking about compound interest, specifically related to a series of monthly investments over a period of time. To find the final amount in Shirley's account after her last deposit on 30 September 2019, with deposits beginning on 30 April 2016, we must use the future value formula for an ordinary annuity because she makes regular deposits at the end of each period. This account pays 9% interest compounded monthly.
To solve this, we need to calculate the total number of deposits made. From April 2016 to September 2019, including both the months of the first and last deposit, Shirley made 42 deposits. The monthly interest rate is 0.09 / 12 (since 9% annual interest is compounded monthly). Using the future value of an annuity formula, we get:
Future Value = Pmt * [((1 + r)^t - 1) / r]
Where:
- Pmt is the monthly payment
- r is the monthly interest rate
- t is the total number of payments
Substituting the values:
Future Value = 60 * [((1 + 0.09/12)^42 - 1) / (0.09/12)]
Calculating the powers and the division, we would arrive at the final amount in Shirley's account immediately after her last deposit. We can illustrate the power of compound interest by comparing the end amount with the sum of the deposits alone to highlight how compound interest helps the investment grow over time.