Question

You're prepared to make monthly payments of $320, 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 $24,354?

Answer 1

You would have made 58.00 payments

Step-by-step explanation:

From the given information:

The future value of the annuity =
`Pmt * [((1+rate)^t-1)/(rate)]`

`24354 = 320 * [((1+(0.11)/(12))^t -1 )/((0.11)/(12))]`

`76.11 = [((1+(0.11)/(12))^t -1 )/((0.11)/(12))]`

`76.11 * {(0.11)/(12) = [{(1+(0.11)/(12))^t -1}]`

`(1+ (76.11 * {(0.11)/(12))) = [{(1+(0.11)/(12))^t }]`

`In (1+ (76.11 * {(0.11)/(12))) = t \ In [{(1+(0.11)/(12))}]`

`\mathtt{t = \frac{In (1+ (76.11 * {(0.11)/(12))}} { In [(1+ (0.11)/(12)]}}}`

t = 58.00