2) If you require a 9 percent return on your investments, which would you prefer?
A.) $5,000 today
B.) $15,000 five years from now
=
= $9,748.97
C.) $1,000 per year for 15 yrs
=
=$8,060.69
Therefore, I would prefer option B since it has the highest present value
4) The Mutual Assurance and Life Company is offering an insurance policy under either of the following two terms:
A. Make a series of 12 payments of $1,200 at the beginning of each of the next 12 years (the first payment being made today)
This is an Annuity Due (Payments occurring at the beginning of the period.
= $9,043.29
PV of an Annuity Due = PV of Ordinary Annuity × (1+r)
= $9,043.29 × (1.08)
= $9,766.76
B. Make a single lump-sum payment today of $10,000 and receive coverage for the next 12 years
If you had investment opportunities offering an 8 % annual return, which alternative would you prefer?
I would choose the series of annual payments for 12 years as this option has a lower present value.
13) You decide to purchase a building for $30,000 by paying $5,000 down and assuming a mortgage of $25k. The bank offers you a 15-year mortgage requiring annual end-of-year payments of $3188 each. The bank also requires you to pay a 3percent loan origination fee, which will reduce the effective amount the bank lends to you. Compute the annual percentage rate of interest on this loan?
PVAN0 = $30,000 - $5,000(down) - $750 (loan origination fee)
= $24,250
Origination fee = 0.03 x $25,000 = $750
$24,250 = $3,188(PVIFAi,15)
PVIFAi,15 = 7.607
Therefore, i 10% from Table IV
17) Construct a loan amortization schedule for a 3-year, 11 percent loan of $30k. The loan requires three equal, end-of-year payments.
$30,000 = PMT(PVIFA.11,3) = PMT(2.444)
PMT = $12,275
End of Year PMT(Payment) Interest Principal Balance Remaining
0 - - - $30,000
1 $12,275 $3,300 $8,975 21,025
2 12,275 2,313 9,962 11,063
3 12,275 1,217 11,058 5*
* difference from zero due to rounding in tables
26) ira investments develops retirement programs for individuals. you are 30 years old and plan to retire on your 60th birthday. You want to establish a plan with IRA that will require a series of equal, annual, end-of-year deposits into the retirement acct. The first deposit will be made 1 year from today on your 31st birthday. The final payment on the acct will be made on your 60th birthday. The retirement plan will allow you to withdraw $120k per year for 15 years with the first withdrawal on your 61st birthday. Also at the end of the 15 year you wish to withdraw an additional $250k. The retirement account promise to earn 12% annually. What periodic payments must be made into the account to achieve your retirement objective?
Amount needed in account after final deposit on your 60th birthday:
PV0 = $120,000(PVIFA.12,15) + $250,000(PVIF.12,15)
PV0 = $120,000(6.811) + $250,000(0.183)
PV0 = $863,070
$863,070 = PMT(FVIFA.12,30) = PMT(241.333)
PMT = $3,576
30)Crab State Bank has offered you a $1,000,000 5-year loan at an interest rate of 11.25 percent, requiring equal annual end-of-year payments that include both principle and interest on the unpaid balance. Develop an amortization schedule for this loan.
$1,000,000 = PMT (PVIFA0.1125, 5)
PMT = $272,274 (by calculator)
End ofYear / Payment / Interest / Principal / Balance Remaining
0 / -- / -- / -- / $1,000,000
1 / $272,274 / $112,500 / $159,774 / 840,226
2 / 272,274 / 94,525 / 177,749 / 662,477
3 / 272,274 / 74,529 / 197,745 / 464,732
4 / 272,274 / 52,282 / 219,992 / 244,740
5 / 272,274 / 27533 / 244,741 / -1*
*Differs from $0 due to rounding.
37) using an online mortgage calculator (see solve for the monthly savings and the number of months it takes to recoup the refinancing costs in problem 34. Hint under the question “what will it cost you?” enter 2850 for “Other” and 0 for all other items
Monthly savings = $81.79
Number of months to recoup costs = 34.8 months.
New monthly payment / $ 831.87Monthly savings / $81.79
Difference in interest / $ 19630.67
Total cost: / $ 2850
Months to recoup costs: / 34.8
Problem 34 (the Humphreys have 20 years remaining on their home mortgage loan. the loan balance is $125,000. the interest rate on the loan is 6.25 percent per year and their current monthly payment is $913.66. The Humphreys have been wondering if they should consider refinancing their mortgage loan as interest rates have fallen. After calling some banks Mrs. Humphreys found that she could get a loan for $125, 000mwith a maturity of 20 years at a rate if 5.1 percent per year. The refinancing will require that the Humphreys pay closing costs of $2,850. If the monthly savings in payments can be invested at 6 percent per year, would you recommend that the Humphreys refinance their home? Assume monthly compounding in solving this problem)
38) Use an online savings or retirement calculator (see to solve the following problem: You are now 30 years old and would like to accumulate $2,000,000 in your retirement account at the age of 65. You currently have $50,000 saved in the retirement account. How much must you set aside at the end of each year over the next 35 years to attain your retirement goal if the account earns 6.5 percent per year? How much would you have to set aside each year if you currently have a zero balance in the retirement account?
I should set aside $12,048 annually if I had $50,000 in my account, and would set $15,576 annually if I had zero balance in the retirement account.
40)Using one of the mortgage loan calculators available on the internet (see a loan amortization for a $150,000, 30-year mortgage loan at a rate of 5 percent and answer the following questions?
- How much is the monthly payment?
$805.23
- How much of the first payment (i.e., year 1, month 1) goes towards the interest? How much towards principal reduction?
$625 goes towards interest, and $180.23 goes towards principal.
- How much of the 180 payment (i.e., year 15, month 12) goes towards interest? How much towards principal reduction?
$425.86 goes towards interest, and $379.38 goes towards principal
- What is the remaining balance on the loan at the end of the fifth year?
$137,743.10