CHAPTER 3 - EXTRA QUESTIONS
MATH 253 THEORY OF INTEREST
CHAPTER 6 - EXTRA QUESTIONS
1. Joan gets a loan of $15,000. She will repay it with quarterly payments at the end of each quarter for 15 years. Interest is at the nominal rate of 6% compounded quarterly. What is the outstanding balance at time t=16? Use the retrospective and prospective methods.
2. Laurel gets a loan of 15,000. She plans to pay it back with annual payments starting at 1000 and increasing by 5% each year. Calculate the term of the loan and the outstanding balance at time t=4. Interest is at the nominal rate of 8% convertible semiannually.
3. Brad gets a loan of 15,000. He plans to pay it back with 20 annual payments, At time t=4, he makes an extra payment of 1500 along with the regular payment. Interest is at the nominal rate of 8% compounded quarterly. Calculate the original annual payment, and the revised payment after the extra payment assuming no change in the term of the loan.
4. Develop the amortization table for a loan of 2500, payable over 6 years at 6% interest.
5. Kathy gets a loan of 8000. She makes semiannual payments of 800 until the loan is paid off. The interest rate is 8% convertible semiannually. Calculate the principal and interest in the 6th payment.
6. Bob gets a loan of 10,000. He pays interest annually to the lender at 8%. He also accumulates a sinking fund over 6 years to pay off the principal on the loan. The sinking fund earns interest at 7%. Calculate his total annual payment.
What is the net interest in the 4th annual payment? What is the net loan at t=4?
7. Greg gets a loan of 10,000, and pays it back with payments starting at 1000 and increasing by 10% each payment. The interest on the loan is at 6%. Find the principal and interest in the 4th payment.
8. Ken gets a loan, and repays it over 8 years with annual payments starting at 100, and increasing by 10 each year. Interest on the loan is at an annual effective rate of 4%. Calculate the amount of the loan. Find the principal and interest in the 6th payment.
1. [pic] [pic] [pic]
At t=16, Prospective [pic]
Retrospective [pic]
2 Term: [pic] [pic]
[pic]
(or prospective) [pic] (note that at t=4, the next payment will be 1000 (1.05)4, so it is the ‘base payment level’ for the remaining payments.
3. [pic] where [pic] [pic]
At t=4, [pic] [pic]
[pic] [pic]
4. [pic] [pic]
|Period |Payment |Interest Paid |Principal Paid |O/S Loan Balance |
|0 | | | |2500 |
|1 |508.41 |150 |358.41 |2141.59 |
|2 |508.41 |128.5 |379.91 |1761.68 |
|3 |508.41 |105.7 |402.71 |1358.97 |
|4 |508.41 |81.54 |426.87 |932.1 |
|5 |508.41 |55.93 |452.48 |479.62 |
|6 |508.41 |28.78 |479.63 |-0.01 |
| | | | | |
| |3050.46 |550.45 |2500.01 | |
5. [pic] [pic] Balance at t=5 [pic]
Interest in 6th payment [pic] Principal [pic]
CHECK: Balance at t=6 [pic] [pic]
6. [pic] [pic] [pic] [pic]
Sinking Fund balance at t=3 [pic]
Interest at t=4 4494.30(.07)=314.60 net interest=800-314.60=485.40
Sinking fund at t=4 [pic]
Net Loan [pic]
7. [pic] (n=9.08; but not necessary to find this to do question.)
Balance at t=3; [pic]
Interest in 4th payment; [pic]4
4th payment; [pic]
Principal; 1331-504.63=826.37
8. [pic]
(You should draw a time diagram to see amount of each payment at time t)
Balance at t=5 [pic] (p.v. of remaining payments)
Or [pic]
Or [pic]
Interest in 6th payment .04(443.29)=17.73 Principal 150-17.73=132.27
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