Final answer:
To calculate the total amount in Nicky's savings account after the last deposit, we determine the future value of her initial deposit and the future value of her monthly deposits using the formulas for compound interest and annuity, respectively. Then, we add both amounts to get the total savings.
Step-by-step explanation:
Calculating the Future Value of Savings Account
To determine the amount in Nicky's savings account immediately after her last deposit on 30 September 2021, we need to calculate the future value of a series of monthly deposits (ordinary annuity), in addition to the future value of the initial deposit. Since the interest is compounded monthly, we will use the future value formula for an annuity:
FV = Pmt * [((1 + r)^n - 1) / r]
Where:
FV = Future Value of the annuity
Pmt = Monthly payment amount
r = Monthly interest rate (annual interest rate / 12)
n = Total number of payments
For Nicky's account:
Pmt = R700
r = 15% / 12 per month = 0.0125
n = 18 payments (Apr 2020 to Sep 2021)
The future value of her monthly deposits (FV_annuity) can be calculated as follows:
FV_annuity = R700 * [((1 + 0.0125)^18 - 1) / 0.0125]
Additionally, the initial deposit of R1000 will also earn interest for 18 months. Its future value (FV_initial) will be:
FV_initial = P * (1 + r)^n
Where:
P = Initial deposit
For the initial deposit:
P = R1000
r = 0.0125 (monthly interest rate)
n = 18 months
FV_initial = R1000 * (1 + 0.0125)^18
Finally, to find the total amount in the account after the last deposit, we add both future values:
Total = FV_annuity + FV_initial
After the calculations, we plug in the values and calculate the final amount.