Question

Calculate the present value of the annuity. (Round your answer to the nearest cent.)

Answer 1

Answer:

Ans. the present value of $1,300/month, at 6.4% compounded monthly for 360 months (30 years) is $207,831.77

Step-by-step explanation:

Hi, first, we have to turn that 6.4% compound monthly rate into an effective rate, one that meets the units of the payment, in our case, effective monthly, that is:

$r(EffectiveMonthly)=\frac{r(CompMonthly)}{12} =\frac{0.063}{12} =0.005333$

Therefore, our effective monthly rate is 0.5333%, and clearly the time of the investment is 30 years*12months=360 months.

Now, we need to use the following formula.

$Present Value=\frac{A((1+r)^{n}-1) }{r(1+r)^{n} }$

Everything should look like this.

$Present Value=\frac{1,300((1+0.005333)^{360}-1) }{0.005333(1+0.005333)^{360} }$

Therefore

$PresentValue=207,831.77$

Best of luck.