Final answer:
To calculate the equivalent present amount of a series of quarterly deposits into an account, you need to calculate the future value of each deposit and then discount them back to the present using the compound interest formula. In this case, the nominal annual rate is 9% compounded quarterly and the investment period is 5 years. The deposits are $800 per quarter.
Step-by-step explanation:
To find the equivalent present amount of a series of deposits into an account, we need to calculate the future value of each deposit and then discount them back to the present using the compound interest formula.
In this case, the nominal annual rate is 9% and interest is compounded quarterly.
The investment period is 5 years (20 quarters) and the deposits are $800 per quarter.
First, we find the future value of each deposit using the compound interest formula:
Future Value = Deposit Amount × (1 + (Nominal Annual Rate / n))^nt
Where:
- Deposit Amount = $800
- Nominal Annual Rate = 9% = 0.09
- n = number of compounding periods per year = 4 (quarterly)
- t = number of years = 5
Now, we calculate the future value of each deposit:
First Deposit Future Value = $800 × (1 + (0.09 / 4))^4*1 = $800 × (1.0225)^4 = $800 × 1.092377521.
Next, we calculate the future value of the second deposit:
Second Deposit Future Value = $800 × (1 + (0.09 / 4))^4*2 = $800 × (1.0225)^8 = $800 × 1.189813984.
Continue this process for all 20 deposits and find their respective future values.
Next, we discount each future value back to the present:
Equivalent Present Amount = Sum of all discounted future values = FV1 / (1 + i) + FV2 / (1 + i)^2 + ... + FV20 / (1 + i)^20, where i is the nominal annual interest rate divided by the number of compounding periods per year.
We calculate the equivalent present amount using the formula:
Equivalent Present Amount = FV1 / (1 + i) + FV2 / (1 + i)^2 + ... + FV20 / (1 + i)^20
Now, plug in the calculated future values: