Consider two loans. Loan A has an initial principal of P₀ and an annual nominal interest rate of i, convertible monthly. Loan B also has an annual nominal interest rate of i, but the interest is convertible daily. At the end of the first month, a payment of m is made on Loan A, which includes one month of interest. The remaining balance on Loan A is then P₁ . Let j be the monthly effective interest rate of Loan B, assuming there are 12 equal months in a year and 365 days in a year.

Determine which of the following represents j.

• [[math]]\quad\left[1+\frac{1}{12}\left(\frac{P_1-P_0+m}{P_0}\right)\right]^{12}-1[[/math]]
• [[math]]\left[1+12\left(\frac{P_1-P_0+m}{P_0}\right)\right]^{1 / 12}-1[[/math]]
• [[math]]\left[1+\frac{12}{365}\left(\frac{P_1-P_0+m}{P_0}\right)\right]^{12}-1[[/math]]
• [[math]]\left[1+\frac{365}{12}\left(\frac{P_1-P_0+m}{P_0}\right)\right]^{12 / 365}-1[[/math]]
• [[math]]\quad\left[1+\frac{12}{365}\left(\frac{P_1-P_0+m}{P_0}\right)\right]^{365 / 12}-1[[/math]]

A borrower planned to repay a loan of L with level payments at the end of each month for 30 years. The loan had an annual nominal interest rate of 6%, convertible monthly. Starting with the 181st payment, the borrower increased the monthly payment to 2000, which enabled the borrower to pay off the loan five years earlier than planned.

Calculate L.

• 253,554
• 277,772
• 310,414
• 330,347
• 333,583

A 100,000 loan has an annual nominal interest rate of 8% convertible quarterly. The loan will be repaid with quarterly payments and the first payment is due three months from the date of the loan. For the first five years each payment will be 2500. All payments thereafter will be 5000 except for a final balloon payment, which will be less than 10,000.

Calculate the balloon payment

• 7920
• 8078
• 9056
• 9154
• 9237

A debt is amortized with 60 equal monthly payments at an annual effective interest rate of 12%. The amount of principal in the third payment is 900.

Calculate the amount of principal in the 33rd payment.

• 668
• 900
• 1008
• 1195
• 1213

A loan of amount [math]a_{\overline{4}|i}[/math] is repaid with payments of 1 at the end of each year for four years. The sum of the interest paid in the last two years is equal to [math](1+i)^2[/math] times the sum of the principal repaid in the first two years.

Calculate i.

• 0.543
• 0.567
• 0.592
• 0.618
• 0.645

An investor deposits 1000 at the beginning of each year for 20 years. The fund earns interest at an annual effective rate of 9.25%. At the end of 20 years, the investor wishes to use the fund to purchase a 30-year annuity-due with monthly payments of 500 based on an annual nominal interest rate of 10% convertible monthly.

Calculate the balance, if any, in the fund after paying for the annuity.

• The fund balance is insufficient to purchase the annuity.
• 0
• 35
• 370
• 510

A loan with an annual nominal interest rate of 9%, convertible monthly, is repaid with 60 monthly payments. The first payment is 1000 and each succeeding payment is 2% less than the previous payment.

Calculate the outstanding loan balance immediately after the 40 th payment is made

• 6889
• 7289
• 7344
• 7407
• 7862

A 15-year loan with an annual effective interest rate of 6% has payments of 400 at the end of each year. At the time of the fifth payment, the borrower pays an extra 1000 and then repays the balance over five years with a revised annual payment of X.

Calculate X.

• 264.13
• 435.38
• 461.51
• 556.46
• 698.90

A loan of 1500 is to be repaid with payments made at the end of each year for 20 years. There are two repayment options:

1. equal payments at an annual effective interest rate of 5%
2. nonlevel payments of interest on the unpaid balance at an annual effective interest rate of i, plus 75 of principal

The sum of the payments is the same under the two options.

Calculate i.

• 5.26%
• 5.51%
• 5.76%
• 6.01%
• 6.26%

On the first of the month, Chuck took out a business loan for 50,000, with payments at the end of each month based on an annual nominal interest rate compounded monthly. Each monthly payment is equal to 800, except for a final drop payment. Immediately after the first payment the balance owed was 49,800.

Calculate the number of payments that Chuck needed to pay off the loan.

• 115
• 117
• 119
• 121
• 123