- #1
What is the correct formula for calculating savings plan?
- MHB
- Thread starter Ladybug101
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In summary, the first formula would yield a $p$ value of 30,000 at the end of the 5 years, while the second formula would yield a $p$ value of 36,000 at the end of the 5 years.
- #2
jonah1
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Beer induced opinions follow. In no event shall the wandering math knight-errant Sir jonah in his inebriated state be liable to anyone for special, collateral, incidental, or consequential damages in connection with or arising out of the use of his beer inspired views.
Alas Milady, that formula you gave is incorrect.
That should either be
\(\displaystyle S_{Ordinary}=p\frac{\left(1+\frac{r}{n}\right)^{ny}-1}{\frac{r}{n}}\)
OR
\(\displaystyle S_{Due}=p\frac{\left(1+\frac{r}{n}\right)^{ny}-1}{\frac{r}{n}}\left(1+\frac{r}{n}\right)\)
where we replace $A$ (which denotes the present value) with $S$ (which denotes the future value).
It depends upon when you plan to make your monthly deposit, that is, at the end of the month (1st formula, future value of an ordinary annuity or end of period payments/deposits) or at the beginning of the month (very likely, 2nd formula, future value of an annuity due or beginning of period payments/deposits).
The question now is when do you plan to make your monthly deposits - at the beginning of the month or at the end of the month - to accumulate 30,000 at the end of 5 years. After you've made that clarification, it boils down to a mere plug and chug routine. You can try both if you like and compare the resulting $p$'s with your textbook's answer section if your problem is from a textbook.
Ladybug101 said:
Alas Milady, that formula you gave is incorrect.
That should either be
\(\displaystyle S_{Ordinary}=p\frac{\left(1+\frac{r}{n}\right)^{ny}-1}{\frac{r}{n}}\)
OR
\(\displaystyle S_{Due}=p\frac{\left(1+\frac{r}{n}\right)^{ny}-1}{\frac{r}{n}}\left(1+\frac{r}{n}\right)\)
where we replace $A$ (which denotes the present value) with $S$ (which denotes the future value).
It depends upon when you plan to make your monthly deposit, that is, at the end of the month (1st formula, future value of an ordinary annuity or end of period payments/deposits) or at the beginning of the month (very likely, 2nd formula, future value of an annuity due or beginning of period payments/deposits).
The question now is when do you plan to make your monthly deposits - at the beginning of the month or at the end of the month - to accumulate 30,000 at the end of 5 years. After you've made that clarification, it boils down to a mere plug and chug routine. You can try both if you like and compare the resulting $p$'s with your textbook's answer section if your problem is from a textbook.
1. How do I create a savings plan?
To create a savings plan, you first need to determine your financial goals and how much you want to save. Then, decide on a timeframe for your savings plan and set a realistic budget. You can also seek advice from a financial advisor or use online tools to help you create a personalized savings plan.
2. How much should I save each month?
The amount you should save each month depends on your financial goals, income, and expenses. A general rule of thumb is to save at least 10-15% of your income. However, it's important to consider your individual circumstances and adjust the amount accordingly.
3. Where should I keep my savings?
It's recommended to keep your savings in a separate bank account or investment account that is easily accessible in case of emergencies. You can also consider diversifying your savings by investing in stocks, bonds, or other assets.
4. How can I stay motivated to stick to my savings plan?
One way to stay motivated is to set specific and achievable goals for your savings plan. You can also track your progress and celebrate small milestones along the way. Additionally, remind yourself of the long-term benefits of saving and the financial security it can provide.
5. What should I do if I can't save as much as I planned?
If you're unable to save as much as you planned, don't get discouraged. Re-evaluate your budget and see if there are any areas where you can cut back on expenses. You can also consider finding ways to increase your income, such as taking on a side job or negotiating a raise at your current job.
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