How much will $800 deposited into a savings account at the end of each month be worth after 2 years at 6% interest compounded monthly? (2.5pts)
How much will $3,500 deposited at the beginning of each 3-month period be worth after 7 years at 12% interest compounded quarterly?(2.5pts)
What amount must be deposited now to withdraw $200 at the beginning of each month for 3 years if interest is 12% compounded monthly?(2.5pts)
How much must be deposited now to withdraw $4,000 at the end of each year for 20 years if interest is 7% compounded annually?(2.5pts)
For the first question, it sounds like you just need to add 6% every month for two years.
If you can let us know when you make progress on the first question, the other questions should be a little easier.
Thank you (:
To calculate the future value of these savings accounts, we can use the formula for compound interest:
Future Value = Principal * (1 + Interest Rate / Number of Compounding Periods)^(Number of Compounding Periods * Number of Years)
Note: The interest rate and the number of compounding periods need to be in consistent units.
1. For the savings account with $800 deposited at the end of each month, the principal is $800, the interest rate is 6% (or 0.06), and it is compounded monthly (12 compounding periods per year).
Therefore, the number of compounding periods is 12 * 2 = 24 (2 years).
Future Value = $800 * (1 + 0.06 / 12)^(12 * 2)
2. For the savings account with $3,500 deposited at the beginning of each 3-month period, the principal is $3,500, the interest rate is 12% (or 0.12), and it is compounded quarterly (4 compounding periods per year).
Therefore, the number of compounding periods is 4 * 7 = 28 (7 years).
Future Value = $3,500 * (1 + 0.12 / 4)^(4 * 7)
3. To calculate the amount that needs to be deposited now to withdraw $200 at the beginning of each month for 3 years, we need to determine the future value as before.
The principal amount to be deposited now is the future value divided by the present value factor.
Present Value Factor = (1 - (1 + Interest Rate / Number of Compounding Periods)^(- Number of Compounding Periods * Number of Years)) / (Interest Rate / Number of Compounding Periods)
Present Value = $200 * Present Value Factor
4. To calculate the amount that needs to be deposited now to withdraw $4,000 at the end of each year for 20 years, we use the same formula as in question 3.
However, since the withdrawals occur annually, we need to adjust the compounding periods accordingly. Interest is compounded annually.
Present Value = $4,000 * Present Value Factor
By plugging in the values into these formulas, you can calculate the results for each question.