Question

Martha receives $200 on the first of each month. Stewart receives $200 on the last day of each month. Both Martha and Stewart will receive payments for 30 years. The discount rate is 9 percent, compounded monthly. What is the difference in the present value of these two sets of payments?

Answer 1

Instructions are below.

Step-by-step explanation:

Giving the following information:

Martha receives $200 on the first of each month. Stewart receives $200 on the last day of each month. Both Martha and Stewart will receive payments for 30 years. The discount rate is 9 percent, compounded monthly.

To calculate the present value, first, we need to determine the final value.

i= 0.09/12= 0.0075

n= 30*12= 360

Martha:

FV= {A*[(1+i)^n-1]}/i + {[A*(1+i)^n]-A}

A= montlhy payment

FV= {200*[(1.0075^360)-1]}/0.0075 + {[200*(1.0075^360)]-200}

FV= 366,148.70 + 2,746.12

FV= 368,894.82

Now, the present value:

PV= FV/ (1+i)^n

PV= 368,894.82/ 1.0075^360

PV= $25,042.80

Stewart:

FV= {A*[(1+i)^n-1]}/i

A= monthly payment

FV= {200*[(1.0075^360)-1]}/0.0075

FV= 366,148.70

PV= 366,148.70/1.0075^360

PV= $24,856.37

Martha has a higher present value because the interest gest compounded for one more time.