A 25-year loan is being repaid with payments of 1300 at the end of each year. The loan payments are based on an annual effective interest rate of 8%. The borrower pays an additional 4000 at the time of the fifth payment and will repay the remaining balance with a payment of X at the end of each of the subsequent ten years.

Calculate X

• 893
• 1300
• 1306
• 1500
• 1902

A bank lends 100,000 to Sam. The loan is repaid with level payments at the end of each year for 30 years based on an annual effective interest rate of 5%. The bank reinvests the loan payments at an annual effective interest rate of 4%.

Calculate the bank’s annual effective yield rate over the 30-year period

• 4.0%
• 4.1%
• 4.2%
• 4.4%
• 4.5%

A bank issues a loan to be repaid by level end-of-year payments for ten years at an annual effective interest rate of 10%. The bank invests these payments at an annual effective interest rate of 10% for the first four years and 7% for the next six years.

Calculate the bank’s annual effective yield rate on this loan over the ten-year period.

• 7.90%
• 8.20%
• 8.33%
• 8.67%
• 9.10%

Two borrowers obtain loans at the same time. Each loan is for the same amount and is repaid with level end-of month payments. The first borrower is charged a monthly effective interest rate of i and makes payments of P for k months to pay off the loan, where k is a positive integer. The second borrower is charged a monthly effective interest rate of j and makes payments of 120 for 5k months to pay off the loan.

Determine which statement about P is true.

• 400 < P ≤ 450
• 450 < P ≤ 500
• 500 < P ≤ 550
• 550 < P ≤ 600
• 600 < P ≤ 650

A loan of 4000 has an annual effective interest rate of 5%. The loan is repaid by payments of 250 at the end of each year for ten years along with a final balloon payment at the end of the eleventh year.

Calculate the outstanding loan balance at the beginning of the seventh year.

• 3593
• 3660
• 3790
• 3856
• 3910

A 15-year loan of 60,000 is to be repaid with payments of X at the end of each month based on an annual nominal interest rate of 7.5%, convertible monthly. When the loan balance is 49,893, the loan is refinanced at an annual nominal interest rate of 6.0%, convertible monthly. Payments remain at X and are paid at the end of each month for as long as necessary, with a smaller final payment.

Calculate the total number of payments, including the smaller final payment.

• 162
• 164
• 166
• 168
• 170

A loan of X is repaid with level payments of R payable at the end of each year for n years. You are given:

i) The interest paid in year 1 is 797.50.

ii) The principal repaid in year n – 4 is 865.

iii) The principal outstanding at the end of year n – 1 is 1144.50.

Determine X

• 9,500
• 10,000
• 10,500
• 11,000
• 11,500

A homeowner borrows 1000 to be repaid with payments at the end of each year for 20 years. There are two repayment options. The first option is equal annual payments based on an annual effective interest rate of 3%. The second option is payments of 50 each year plus interest on the unpaid balance at an annual effective interest rate of i. The total payments under the two options are the same.

Calculate i.

• 2.86%
• 3.00%
• 3.28%
• 3.44%
• 4.76%

A 20-year loan of 500 based on a 5% annual effective interest rate is repaid with level installments at the end of each year.

Determine the installment in which the principal and interest portions are most nearly equal to each other.

• 1st
• 7th
• 10th
• 13th
• 20th

A debt is amortized with 120 level payments at the end of each month based on an annual effective interest rate of 8%. The amount of principal in the sixth payment is 600.

Calculate the amount of principal in the 24th payment.

• 532
• 673
• 700
• 704
• 784