MHB What is the correct formula for calculating savings plan?

[Ladybug101]

Hello! I am having trouble with this question. Please look at the image. I understand that I’m supposed to use the A = p *(1 + r/n) [(1 + r/n)n*y - 1] / (r/n) formula but I’m really stuck on this problem.

 

[jonah1]

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Hello! I am having trouble with this question. Please look at the image. I understand that I’m supposed to use the A = p *(1 + r/n) [(1 + r/n)n*y - 1] / (r/n) formula but I’m really stuck on this problem.

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.