How much money should be deposited into an account that earns 4.6% interest, compounded every month, so that after 20 years there is a balance of $24,000?
+118613 FV=P(1+i)^n
i=0.046/12=0.003833333333
n=20*12 = 240
FV=24000
$${\frac{{\mathtt{24\,000}}}{\left({\left({\mathtt{1.003\: \!833\: \!333\: \!333\: \!333\: \!3}}\right)}^{{\mathtt{240}}}\right)}} = {\mathtt{9\,581.294\: \!137\: \!691\: \!544\: \!508\: \!7}}$$
$9581.30 must be invested
Note: This is assuming that 4.6% interest is earned every month. As it does not say so exactly, that is what I'm assuming.
24,000=(1.046)20(years)*12(months)*x, where x is initial deposit
24000=(1.046)240*x=48708.4475130686595576*x
$${\frac{{\mathtt{24\,000}}}{{\mathtt{48\,708.447\: \!513\: \!068\: \!659\: \!557\: \!6}}}} = {\mathtt{x}} = {\mathtt{0.492\: \!727\: \!673\: \!029\: \!626\: \!1}}$$
Which about equals 49 cents
+118613 FV=P(1+i)^n
i=0.046/12=0.003833333333
n=20*12 = 240
FV=24000
$${\frac{{\mathtt{24\,000}}}{\left({\left({\mathtt{1.003\: \!833\: \!333\: \!333\: \!333\: \!3}}\right)}^{{\mathtt{240}}}\right)}} = {\mathtt{9\,581.294\: \!137\: \!691\: \!544\: \!508\: \!7}}$$
$9581.30 must be invested
