This is the question: "If you want to have $\$75,000$ after $35$ years in your account that pays $12\%$ annual interest compounded quarterly, how much should you put in as your original investment?"
The formula I'm using is $y = a (1+r)^t$, with $a$ being the initial amount, $r$ being the rate in decimal form, and $t$ is time relative to the rate. Or $y = a (1+r/t)^t$
Although my biggest problem is that I'm not sure whether to have the $1+r$ or $1-r$.
So after plugging in what I have either:
$75000 = a (1-.12)^{35}$
$75000 = a (1+.12)^{35}$
or you can use this formula (preferably):
$75000 = a (1-.12/35)^{35}$
$75000 = a (1+.12/35)^{35}$
$\endgroup$ 41 Answer
$\begingroup$Suppose I deposit $X$ dollars and leave it for say 25 interest-periods gaining 5% per interest period.
Then the amount in my account at the end of that process is $X (1.05)^{25} = 3.386X$
If I know the amount at the end of the period, $Y = 3.386X$ then obviously I can find out what X was also. Say the resulting amount is \$45000 - then the original deposit was $\frac{45000}{3.386} \to$ \$13288.63
Your problem is exactly like this - you just have extra steps to calculate what the interest rate is and how many interest periods you are talking about.
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