1. You are scheduled to receive annual payments of $11,000 for each of the next
ID: 2639538 • Letter: 1
Question
1. You are scheduled to receive annual payments of $11,000 for each of the next 22 years. Your discount rate is 8 percent. What is the difference in the present value if you receive these payments at the beginning of each year rather than at the end of each year?
3. You are considering an annuity which costs $51200 today. The annuity pays $7300 a year. The rate of return is 5 percent. What is the length of the annuity time period? (Do not round intermediate calculations.)
4. Todd is able to pay $330 a month for 6 years for a car. If the annual interest rate is 6.4 percent, how much can Todd afford to borrow to buy a car?
5. You borrow $6,730 to buy a car. The terms of the loan call for monthly payments for 5 years at the annual interest rate of 6 percent. What is the amount of each payment?
1. You are scheduled to receive annual payments of $11,000 for each of the next 22 years. Your discount rate is 8 percent. What is the difference in the present value if you receive these payments at the beginning of each year rather than at the end of each year?
2. What is the future value of $1,070 a year for 4 years at a 6 percent rate of interest?3. You are considering an annuity which costs $51200 today. The annuity pays $7300 a year. The rate of return is 5 percent. What is the length of the annuity time period? (Do not round intermediate calculations.)
4. Todd is able to pay $330 a month for 6 years for a car. If the annual interest rate is 6.4 percent, how much can Todd afford to borrow to buy a car?
5. You borrow $6,730 to buy a car. The terms of the loan call for monthly payments for 5 years at the annual interest rate of 6 percent. What is the amount of each payment?
Explanation / Answer
Answer for question 1:
Difference in Present value = $112,208.18 - $121,184.83 = $8,976.65
Workings are as under:
Answer for Question no 2:
Future value of $1070 for 4 years at a 6 percent rate of interest
=$1,040(1+.06)4 = $1,040 * 1.26247696 = $1,312.976 rounded to $1,312.97
Answer for question no3:
Present value of the annuity =$51,200
rate of interest = 5%
Annual payment = $7,300
Using Nper function in excel one can arrive at the number of periods the amount can be with drawn
=nper(0.05,7300,-51200) = 8.850 = 8.8 years.
Answer for Question 4:
Using PV function of Excel one can arrive at the loan amount
PV(rate/12,nper,payment per period)
=PV(0.064/12,12*6,$330) = $19,686.97
Answer for question 5:
EMI=PMT(.06/12,60,6730) = $130.11
Using PMT function in Excel EMI amount is calculated, the variables required are PMT(r,nper,PV)
r= rate per period
nper = no of periods in the repayment period
PV is the loan amount
Year Amount PV factor for the end of year PV factor at the beginning of the year PV if received at the end of year PV if received at the beginning of the year 1 $11,000.00 0.925925926 1 $10,185.19 $11,000.00 2 $11,000.00 0.85733882 0.925925926 $9,430.73 $10,185.19 3 $11,000.00 0.793832241 0.85733882 $8,732.15 $9,430.73 4 $11,000.00 0.735029853 0.793832241 $8,085.33 $8,732.15 5 $11,000.00 0.680583197 0.735029853 $7,486.42 $8,085.33 6 $11,000.00 0.630169627 0.680583197 $6,931.87 $7,486.42 7 $11,000.00 0.583490395 0.630169627 $6,418.39 $6,931.87 8 $11,000.00 0.540268885 0.583490395 $5,942.96 $6,418.39 9 $11,000.00 0.500248967 0.540268885 $5,502.74 $5,942.96 10 $11,000.00 0.463193488 0.500248967 $5,095.13 $5,502.74 11 $11,000.00 0.428882859 0.463193488 $4,717.71 $5,095.13 12 $11,000.00 0.397113759 0.428882859 $4,368.25 $4,717.71 13 $11,000.00 0.367697925 0.397113759 $4,044.68 $4,368.25 14 $11,000.00 0.340461041 0.367697925 $3,745.07 $4,044.68 15 $11,000.00 0.315241705 0.340461041 $3,467.66 $3,745.07 16 $11,000.00 0.291890468 0.315241705 $3,210.80 $3,467.66 17 $11,000.00 0.270268951 0.291890468 $2,972.96 $3,210.80 18 $11,000.00 0.250249029 0.270268951 $2,752.74 $2,972.96 19 $11,000.00 0.231712064 0.250249029 $2,548.83 $2,752.74 20 $11,000.00 0.214548207 0.231712064 $2,360.03 $2,548.83 21 $11,000.00 0.198655748 0.214548207 $2,185.21 $2,360.03 22 $11,000.00 0.183940507 0.198655748 $2,023.35 $2,185.21 Total $112,208.18 $121,184.83Related Questions
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