To solve the question using a finance calculator, you need to determine the future value of an annuity (the series of deposits Derek will make) and then calculate how much that future value will grow over the additional years until the total 36 years is reached.
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Calculate the future value of the annuity after 17 years:
- N = 17 (the number of years Derek will make the deposits)
- PMT = 2369 (the amount deposited each year)
- i/y = 12% (the annual interest rate)
- FV = ? (we will calculate this after entering the values)
- PV = 0 (since the calculation starts with zero initial balance)
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Calculate the future value (FV1) of the account after 17 years.
Now, using those values in your calculator, you will get FV1 after 17 years.
- Using FV1, calculate the future value over the next 19 years (from year 17 to year 36):
- N = 19 (the number of additional years for compound growth)
- PV = FV1 (the value computed in the previous step)
- i/y = 12% (the same interest rate)
- PMT = 0 (no additional payments are made during this period)
- FV = ? (we will compute the final value)
By calculating the two stages—first finding FV1 and then FV2—you can find out how much will be in the account 36 years from today.
Step-by-Step Calculation:
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Calculate FV1 after 17 years with the annuity:
- N = 17
- PMT = 2369
- i/y = 12%
- PV = 0
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Enter these values into your financial calculator to find FV1.
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Then, use FV1:
- N = 19
- PV = FV1 (from the previous step)
- PMT = 0
- i/y = 12%
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Calculate for FV to find out how much will be there after 36 years.
With these calculations, you will find the total amount in the account after 36 years.