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MHB What is the correct formula for calculating savings plan?
- Thread starter Ladybug101
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SUMMARY
The correct formulas for calculating a savings plan are either S_{Ordinary}=p\frac{\left(1+\frac{r}{n}\right)^{ny}-1}{\frac{r}{n}} for ordinary annuities or S_{Due}=p\frac{\left(1+\frac{r}{n}\right)^{ny}-1}{\frac{r}{n}}\left(1+\frac{r}{n}\right) for annuities due. The choice between these formulas depends on whether deposits are made at the beginning or the end of the month. To accumulate a target amount, it is essential to clarify the timing of deposits, which will dictate the appropriate formula to use.
PREREQUISITES- Understanding of annuities and their types (ordinary vs. due)
- Familiarity with the formula for future value of annuities
- Basic knowledge of interest rates and compounding periods
- Ability to perform algebraic calculations
- Study the future value of ordinary annuities and annuities due in detail
- Practice using the formulas with different interest rates and time periods
- Explore financial calculators that can automate these calculations
- Review examples of savings plans in financial textbooks or online resources
Students studying finance, financial planners, and anyone looking to understand savings plans and annuity calculations.
- #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
$$S_{Ordinary}=p\frac{\left(1+\frac{r}{n}\right)^{ny}-1}{\frac{r}{n}}$$
OR
$$S_{Due}=p\frac{\left(1+\frac{r}{n}\right)^{ny}-1}{\frac{r}{n}}\left(1+\frac{r}{n}\right)$$
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
$$S_{Ordinary}=p\frac{\left(1+\frac{r}{n}\right)^{ny}-1}{\frac{r}{n}}$$
OR
$$S_{Due}=p\frac{\left(1+\frac{r}{n}\right)^{ny}-1}{\frac{r}{n}}\left(1+\frac{r}{n}\right)$$
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.
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