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

Answer:

You would have made  58.00 payments

Explanation:

From the given information:

The future value of the annuity   = $Pmt \times [\dfrac{(1+rate)^t-1}{rate}]$

$24354 = 320 \times [\dfrac{(1+\dfrac{0.11}{12})^t -1 }{\dfrac{0.11}{12}}]$

$76.11 = [\dfrac{(1+\dfrac{0.11}{12})^t -1 }{\dfrac{0.11}{12}}]$

$76.11 \times {\dfrac{0.11}{12} = [{(1+\dfrac{0.11}{12})^t -1}]$

$(1+ (76.11 \times {\dfrac{0.11}{12})) = [{(1+\dfrac{0.11}{12})^t }]$

$In (1+ (76.11 \times {\dfrac{0.11}{12})) = t \ In [{(1+\dfrac{0.11}{12})}]$

$\mathtt{t = \dfrac{In (1+ (76.11 \times {\dfrac{0.11}{12})}} { In [(1+ \dfrac{0.11}{12}]}}}$

t = 58.00