You're prepared to make monthly payments of $330, beginning at the end of this month, into an account that pays 11 percent interest compounded monthly. How many payments will you have made when your account balance reaches $21,334?

the number of payment is 56

Explanation:

The computation of the number of payment made is shown below:

As we know that

Future value of annuity = Payment per period × [(1 + rate of interest)^number of payments - 1] ÷ rate of interest  

$24,000 = $330 × [(1 + (11% ÷ 12))^n - 1] ÷ (11% ÷ 12)

$24,000 = $330 × [(1 +0.00916666666)^n - 1] ÷ 0.00916666666

1 +0.00916666666)^n - 1 = ( $24,000 × 0.00916666666 ) ÷ ($330)

(1 + 0.00916666666)^n - 1 = 0.66666666

(1.00916666666)^n = 1.6666666

Now take the log on both sides

n = log (1.66666666618) ÷ log (1.00916666666)

n = 56

hence, the number of payment is 56

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