Molly opened a bank account. She deposited $86.50 into her account every month for 20 months. She used $24.50 every month to pay for singing lessons. After 20 months, she used of the total money left in her account to go to a summer camp for singers. What is the total amount of money Molly spent to go to the summer camp?

Over 20 months, Molly deposited a total of 20 * $86.50 = $<<20*86.5=1730>>1730 into her bank account.

She spent a total of 20 * $24.50 = $<<20*24.5=490>>490 on singing lessons.
So she had $1730 - $490 = $<<1730-490=1240>>1240 left in her account after 20 months.
She used 1/3 * $1240 = $<<1240*1/3=413.33>>413.33 to go to the summer camp. Answer: \boxed{413}.