Question

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

$1300 monthly at 6.4% for 30 years

Answer 1

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

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)=(r(CompMonthly))/(12) =(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=(A((1+r)^(n)-1) )/(r(1+r)^(n) )`

Everything should look like this.

`Present Value=(1,300((1+0.005333)^(360)-1) )/(0.005333(1+0.005333)^(360) )`

Therefore

`PresentValue=207,831.77`

Best of luck.