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?

Instructions are below.

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.