Answer:
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
<u>Martha:</u>
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
<u>Stewart:</u>
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.
