Question

In: Finance

John has taken out a $10,000 loan, which is being repaid with 30 level annual payments....

John has taken out a $10,000 loan, which is being repaid with 30 level annual payments. The first payment will be one year from now. John pays an additional $500 during the fourth and twelfth payments. Following the two additional payments, the loan is repaid by annual payments of the original size with a larger final payment after the last full repayment.

If the effective annual interest rate is 5%, what is the amount of the larger payment?

A. 480

B. 640

C. 800

D. 970

E. 1130

Solutions

Expert Solution

Let the annual Normal payment be ''A''

Hence

Present value of the Loan =

=>A or Annual Payment = $650.514

Repayment schedule-

A B=A*5% C A+B-C
Year Opening loan Balance Interest@5% Payment Closing loan
1 10000.000 500.000 650.514 9849.486
2 9849.486 492.474 650.514 9691.446
3 9691.446 484.572 650.514 9525.505
4 9525.505 476.275 1150.514 8851.266
5 8851.266 442.563 650.514 8643.315
6 8643.315 432.166 650.514 8424.967
7 8424.967 421.248 650.514 8195.701
8 8195.701 409.785 650.514 7954.972
9 7954.972 397.749 650.514 7702.207
10 7702.207 385.110 650.514 7436.803
11 7436.803 371.840 650.514 7158.129
12 7158.129 357.906 1150.514 6365.522
13 6365.522 318.276 650.514 6033.284
14 6033.284 301.664 650.514 5684.434
15 5684.434 284.222 650.514 5318.142
16 5318.142 265.907 650.514 4933.535
17 4933.535 246.677 650.514 4529.698
18 4529.698 226.485 650.514 4105.669
19 4105.669 205.283 650.514 3660.438
20 3660.438 183.022 650.514 3192.946
21 3192.946 159.647 650.514 2702.079
22 2702.079 135.104 650.514 2186.669
23 2186.669 109.333 650.514 1645.489
24 1645.489 82.274 650.514 1077.249
25 1077.249 53.862 650.514 480.598
26 480.598 24.030 650.514 -145.887
27 -145.887 -7.294 650.514 -803.695
28 -803.695 -40.185 650.514 -1494.394
29 -1494.394 -74.720 650.514 -2219.627
30 -2219.627 -110.981 650.514 -2981.123

As we can see the loan balance is negative from year 26, due to additional payment in year 4 and 12.

hence a lumpsum or large payment to be made at year 25th End to close the loan account.

Lumpsum amount to be paid a year 25th end = 650.514+480.598 = 1130 approx

Correct Answer-E. 1130

Payment schedule if 1130 is paid at the end 25th year-

A B=A*5% C A+B-C
Year Opening loan Balance Interest@5% Payment Closing loan
1 10000.000 500.000 650.514 9849.486
2 9849.486 492.474 650.514 9691.446
3 9691.446 484.572 650.514 9525.505
4 9525.505 476.275 1150.514 8851.266
5 8851.266 442.563 650.514 8643.315
6 8643.315 432.166 650.514 8424.967
7 8424.967 421.248 650.514 8195.701
8 8195.701 409.785 650.514 7954.972
9 7954.972 397.749 650.514 7702.207
10 7702.207 385.110 650.514 7436.803
11 7436.803 371.840 650.514 7158.129
12 7158.129 357.906 1150.514 6365.522
13 6365.522 318.276 650.514 6033.284
14 6033.284 301.664 650.514 5684.434
15 5684.434 284.222 650.514 5318.142
16 5318.142 265.907 650.514 4933.535
17 4933.535 246.677 650.514 4529.698
18 4529.698 226.485 650.514 4105.669
19 4105.669 205.283 650.514 3660.438
20 3660.438 183.022 650.514 3192.946
21 3192.946 159.647 650.514 2702.079
22 2702.079 135.104 650.514 2186.669
23 2186.669 109.333 650.514 1645.489
24 1645.489 82.274 650.514 1077.249
25 1077.249 53.862 1130.000 0

jeff jeffy answered 2 years ago
Next > < Previous

Related Solutions

James has a loan of 10,000, which is to be repaid with 10 level annual payments...
James has a loan of 10,000, which is to be repaid with 10 level annual payments at an annual effective interest rate of 14.5%. Calculate the Macaulay duration of the loan using the 14.5% interest rate.
James has a loan of 10,000, which is to be repaid with 10 level annual payments...
James has a loan of 10,000, which is to be repaid with 10 level annual payments at an annual effective interest rate of 14.5%. Calculate the Macaulay duration of the loan using the 14.5% interest rate.
A loan of $10,000 is being repaid with 10 payments at the end of each year,...
A loan of $10,000 is being repaid with 10 payments at the end of each year, where each payment includes equal amount of repayment of the principal and the interest at a rate of 5% based on the outstanding balance after the previous payment. Immediately after the loan was made, the right of the loan was sold at a price that yields an annual effective rate of 10%. Find the price paid for the right of the loan. (Answer: $8072.28)...
A loan of $10,000 is to be repaid with 10 semi-annual payments. The first payment is...
A loan of $10,000 is to be repaid with 10 semi-annual payments. The first payment is X in 6 months time. i(2) = 4%. Find X if a) Payments increase by $100 every 6 months. b) Payments increase by 10% every 6 months.
A $1000 loan is being repaid with level payments at the end of each year for...
A $1000 loan is being repaid with level payments at the end of each year for 4 years using a sinking fund method. The loan has 10% effective interest per year and the sinking fund has 8% interest per year. Create a sinking fund table for this payment plan. Include a column for the period, interest paid that period, sinking fund deposit that period, interest earned in the sinking fund that period and the balance in the sinking fund at...
A loan of €50,000 is being repaid with monthly level payments at the end of each...
A loan of €50,000 is being repaid with monthly level payments at the end of each year for 6 years at 5% effective rate. Just after making the payment of the second annuity, it is decided to change the amortization method, the loan is being repaid with constant annual principal repayments for the remaining 3 years at an interest rate of 4.5%. A) find the outstanding debt just after the payment of the third annuity
A loan of €50,000 is being repaid with monthly level payments at the end of each...
A loan of €50,000 is being repaid with monthly level payments at the end of each year for 6 years at 5% effective rate. Just after making the payment of the second annuity, it is decided to change the amortization method, the loan is being repaid with constant annual principal repayments for the remaining 3 years at an interest rate of 4.5%. find the outstanding debt just after the payment of the third annuity
Donald takes out a loan to be repaid with annual payments of $500 at the end...
Donald takes out a loan to be repaid with annual payments of $500 at the end of each year for 2n years. The annual effective interest rate is 4.94%. The sum of the interest paid in year 1 plus the interest paid in year n + 1 is equal to $720. Calculate the amount of interest paid in year 10.
A 18 year loan is being repaid with level payments at the end of each month....
A 18 year loan is being repaid with level payments at the end of each month. The loan rate of interest is 15.6% compounded monthly. In which month is the interest portion approximately equal to 5 times principal the portion? Give an integer answer.
Eve borrows 10,000. The loan is being repaid with the following sequence of monthly payments: 100,...
Eve borrows 10,000. The loan is being repaid with the following sequence of monthly payments: 100, 150, 100, 150, 100, 150, etc. The annual nominal interest rate is 7.56% payable monthly. Calculate the amount of principal repaid in the 13th payment.
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT