Respuesta :
Answer:
Ans. the amount of time needed for the sinking fund to reach $25,000 if invested $255/month at 5.8% compounded monthly (Effective monthly=0.4833%) is 80.45 months.
Step-by-step explanation:
Hi, first we need to transform that 5.8% compounded monthly into an effective monthly rate, that is as follows.
[tex]r(EffectiveMonthly)=\frac{r(Comp.Monthly)}{12} =\frac{0.058}{12} =0.00483[/tex]
That means that our effective monthly rate is 0.483%
Now, we need to solve for "n" the following formula.
[tex]FutureValue=\frac{A((1+r)^{n}-1) }{r}[/tex]
Let´s start solving
[tex]25,000=\frac{255((1.00483)^{n}-1) }{0.00483}[/tex]
[tex]\frac{25,000*0.00483}{255} =1.00483^{n} -1\\[/tex]
[tex]0.47352941=1.00483^{n} -1[/tex]
[tex]1+0.47352941=1.00483^{n[/tex]
[tex]1.47352941=1.00483^{n}[/tex]
[tex]Ln(1.47352941)=n*Ln(1.00483)[/tex]
[tex]\frac{Ln(1.47352941)}{Ln(1.00483)} =n=80.45[/tex]
This means that it will take 80.45 months to reach $25,000 with an annuity of $255 at a rate of 5.8% compounded monthly (0.4833% effective monthly).
Best of luck.
