A loan of 100 is to have all principal and accrued interest paid at the end of five years. Interest accrues at an annual effective rate of 5\% for the first two years and at a force of interest at time [math]t[/math] in years [math](t\gt2)[/math] of [math]\delta_t=\frac{1}{1+t}[/math].

Calculate the equivalent annual effective rate of discount for the five-year period.

• 10.9%
• 13.0%
• 14.6%
• 15.4%
• 17.1%

Harry borrows 10,000 from Sally and agrees to repay the five-year loan with equal payments at the end of each quarter. Interest on the loan is charged at an annual nominal rate of 6% convertible quarterly. Immediately after the fourth payment, Harry and Sally get married and Sally forgives the remaining debt.

Calculate the total interest payments that Sally forgoes receiving by having forgiven the remaining debt.

• 582
• 951
• 1,088
• 1,270
• 1,769

A loan of 100,000 at an annual effective rate of 9.12% is repaid with level payments at the end of each month over 15 years. Immediately after the 59th payment is made, the outstanding balance is refinanced at an annual effective rate of 5.76%. The term of the refinanced loan is 20 years with level payments at the end of each month.

Calculate the interest portion of the first payment of the refinanced loan.

• 375
• 378
• 381
• 384
• 387

5000 is borrowed at an annual nominal rate of interest of j convertible monthly. The loan is repaid with payments of 291.23 at the end of each quarter for 5 years.

Calculate j.

• 5.97%
• 6.00%
• 6.04%
• 6.09%
• 6.14%

A loan is originally scheduled to be paid in installments of 1000 payable at the end of each month for three years. The amortization is calculated with an annual nominal interest rate of 9% convertible monthly. After paying one full year of scheduled installments, the borrower increases monthly payments to 2000, resulting in a final drop payment.

Calculate the number of months after the first year that it takes for the borrower to pay off the loan.

• 10
• 11
• 12
• 13
• 14

A car dealership offers a 120-month loan for a blue car costing 30,000, with an annual nominal interest rate of 9% compounded monthly and level end-of-month payments. The dealership also offers a loan for a red car costing 33,000, with the same interest rate and end-of-month payments as for the loan for the blue car.

Calculate the number of months needed to pay off the loan for the red car

• 132
• 135
• 138
• 140
• 141

A bank offers a loan to each of two borrowers with different credit scores. Both loans are for the same amount. The first borrower is charged a monthly effective interest rate of 1% and makes level end-of- month payments of X for n months to pay off the loan. The second borrower is charged a monthly effective interest rate of 2.01% and makes level end- of-month payments of 2.01X for 200 months to pay off the loan.

Calculate n.

• 200
• 250
• 300
• 350
• 400

Annual payments of 240 are made at the end of each year to repay a loan of 3400. The payments are based on an annual effective interest rate of 4.5%. The loan is settled with a drop payment of X.

Calculate X.

• 1.61
• 4.53
• 8.83
• 12.48
• 13.04

Juliana takes out a loan for $200,000 with 25 yearly payments at the end of each year. She makes payments which are twice the interest due for the first 24 months and pays off the remaining balance with the 25th payment. If the interest on the loan is 4%, what is the final payment equal to?

• $72,079.34
• $117,167.27
• $78,085.96
• $75,082.65
• Insufficient information to solve problem

Hardiek, Aaron (June 2010). "Study Questions for Actuarial Exam 2/FM". digitalcommons.calpoly.edu. Retrieved November 20, 2023.

Jake buys a $140,000 home. He must make monthly mortgage payments for 40 years, with the first payment to be made a month from now. The annual effective rate of interest is 8%. After 20 years Jake doubles his monthly payment to pay the mortgage off more quickly. Calculate the interest paid over the duration of the loan.

• $241,753.12
• $527,803.12
• $356,440.43
• $136,398.99
• $225,440.43

Hardiek, Aaron (June 2010). "Study Questions for Actuarial Exam 2/FM". digitalcommons.calpoly.edu. Retrieved November 20, 2023.