Question

Hello im stuck on this homework question and need help ty

Answer 1

We have to calculate an annuity with the following characteristics:

• Payment amount: $ 135 (M = 135)

• Subperiod: quarterly (number of subperiods, n = 4)

,

• Interest rate: 4% (r = 0.04)

,

• Period: 4 years (t = 4)

We can now use the formula for the future value (A), as they willl withdraw the money after the 14 years:

`A=M*((1+(r)/(n))^(nt)-1)/((r)/(n))`

We can replace the variables with its values and find A:

`\begin{gathered} A=135*((1+(0.04)/(4))^(4*14)-1)/((0.04)/(4)) \\ A=135*((1.01)^(56)-1)/(0.01) \\ A=135*(1.74580981920691451592-1)/(0.01) \\ A=135*(0.74580981920691451592)/(0.01) \\ A=135*74.850981920691451592 \\ A\approx10068.43 \end{gathered}`

Answer: the future value of the annuity is $10,068.43.