Suppose you are expected to receive $5,000 per month, 10 years from now for 15 years....

Suppose you are expected to receive $5,000 per month, 10 years from now for 15 years. How much you would pay per month for 10 years if you are required to start payment today? (Assume interest rate i⁽¹²⁾ is 6.5%).

Thanks!

Expert Solution

amount per month (P)=   5000
interest rate per month (i)= 6.5%/12=   0.005416666667
total months (n)= 15*12=   180
Value of Annuity at year 10 shall be calculated by Present Value of Annuity Formula
Present Value of ordinary annuity formula = (P *(1-(1/(1+i)^n))/i)
5000*(1-(1/(1+0.00541666667)^180))/0.0054166667
573982.0567

This is required future value of Investment =   573982.0567

We will deposit or make payment starting from today. So it is Annuity due. Future value of Annuity due is $573982.06

Number of deposit in 10 years = 12*10= 120

Future value of annuity due formula = P *(1+i)*{ (1+i)^n - 1 } / i
573982.06 = p*(1+0.00541666667)*(((1+0.005416666667)^120)-1)/0.005416666667

573982.06 =P*   169.315338
P=573982.06/   169.315338
3390.018098
So each month payment required is   $3,390.02

jeff jeffy answered 6 months ago

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Suppose you are expected to receive $5,000 per month, 10 years from now for 15 years....

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