A loan of 5,000,000 is to be repaid by installments of X at the end of each quarter over a period of ten years. The annual nominal interest rate for the loan is 8% compounded quarterly. The actual quarterly payment for the first five years is X rounded up to the next higher 1000. After that, each quarterly payment is X rounded up to the next higher 100,000, until the loan is paid off with a drop payment.

Calculate the total number of payments, including the drop payment, needed to repay the loan.

• 36
• 37
• 38
• 39
• 40

A loan of 50,000 id based on an annual effective interest rate of 6%. You are given:

1. The loan is to be repaid with quarterly payments of 2125 and a final drop payment.
2. The first payment is due 1.5 years after the loan is taken out.

Calculate the number of payments of 2125 to be made.

• 28
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• 30
• 31
• 32

A credit card company charges an annual effective interest rate of 16.8%. Interest accumulates from the date of purchase. A borrower's credit card balance was X at the beginning of month 1. Starting with month 1, the borrower purchased satellite internet service, resulting in a 79.99 charge on the credit card at the middle of each month. The borrower paid 250 at the end of each month. Immediately after the payment in month 15, the balance was 3000.

Determine which of the following is an equation of value that can be used to solve for X.

• [[math]]\quad X+\sum_{n=1}^{15} \frac{79.99}{(1.014)^{n-0.5}}=\frac{3000}{(1.014)^{15}}+\sum_{n=1}^{15} \frac{250}{(1.014)^n}[[/math]]
• [[math]]\quad X+\sum_{n=1}^{16} \frac{79.99}{(1.168)^{\frac{n+0.5}{12}}}=\frac{3000}{(1.168)^{\frac{5}{4}}}+\sum_{n=1}^{16} \frac{250}{(1.168)^{\frac{n}{12}}}[[/math]]
• [[math]]\quad X+\sum_{n=1}^{16} \frac{79.99}{(1.168)^{\frac{n-0.5}{12}}}=\frac{3000}{(1.168)^{\frac{4}{3}}}+\sum_{n=1}^{16} \frac{250}{(1.168)^{\frac{n}{12}}}[[/math]]
• [[math]]\quad X+\sum_{n=1}^{15} \frac{79.99}{(1.168)^{\frac{n+0.5}{12}}}=\frac{3000}{(1.168)^{\frac{5}{4}}}+\sum_{n=1}^{15} \frac{250}{(1.168)^{\frac{n}{12}}}[[/math]]
• [[math]]\quad X+\sum_{n=1}^{15} \frac{79.99}{(1.168)^{\frac{n-0.5}{12}}}=\frac{3000}{(1.168)^{\frac{5}{4}}}+\sum_{n=1}^{15} \frac{250}{(1.168)^{\frac{n}{12}}}[[/math]]

A student takes out a loan for 30,000. The annual nominal interest rate is 9%, convertible semiannually. The student pays off the loan in five years with monthly payments beginning one month from today. The first payment is 500, and each subsequent payment is X more than the previous payment.

Determine which of the following is an equation of value that can be used to solve for X.

• [[math]]\quad 30,000=\sum_{n=0}^{60} \frac{500+n X}{(1.015)^{\frac{n}{2}}}[[/math]]
• [[math]]30,000=\sum_{n=0}^{60} \frac{500+n X}{(1.045)^{\frac{n}{6}}}[[/math]]
• [[math]]30,000=\sum_{n=1}^{60} \frac{500+n X}{(1.045)^{\frac{n}{6}}}[[/math]]
• [[math]]30,000=\sum_{n=1}^{60} \frac{500+(n-1) X}{(1.015)^{\frac{n}{2}}}[[/math]]
• [[math]]\quad 30,000=\sum_{n=1}^{60} \frac{500+(n-1) X}{(1.045)^{\frac{n}{6}}}[[/math]]

A loan of 20,000 is to be repaid with payments at the end of each year for ten years. The first payment is X. Each subsequent payment is 6% greater than the preceding payment. The loan payments are based on an annual effective interest rate of 10%.

Calculate the loan balance immediately after the eighth payment.

• 6685
• 6937
• 7353
• 7794
• 8088

A loan of 20,000 is to be repaid with ten increasing installments payable at the end of each year. Each installment will be 10% greater than the preceding installment. The annual effective interest rate on the loan is 9%.

Calculate the amount of principal in the second installment.

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• 527
• 975
• 1435
• 1774

A purchase of 5020 is paid off with a loan at an annual effective interest rate of 6.25%. Payments are made at the end of each year until the loan is paid off. Each payment is 360 except for a final balloon payment, which is less than 720.

Calculate the amount of the balloon payment.

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• 630
• 649
• 667
• 685

A five-year interest-only loan in the amount of 10,000 has annual payments, and an annual effective interest rate i. At the end of year 5, the borrower pays off the principal along with the last interest payment.

To finance the principal payment, the borrower buys the following two zero-coupon bonds that both mature at the end of year 5.

It costs the borrower a total of 2260.19 at the end of year 3 to pay the interest due and to buy Bond 1.

Calculate i.

• 2.60%
• 3.00%
• 3.18%
• 3.75%
• 4.30%

Bank A lends a certain sum of money at an annual effective interest rate of 7%. The loan is to be repaid by 16 annual payments of 1000, with the first payment due after one year. Immediately after receiving the 8 th payment, Bank A sells the right to receive the remaining 8 payments to Bank B. Bank A’s yield on the entire transaction is an annual effective interest rate of 6%.

Calculate the amount that Bank B paid to assume the loan.

• 5159
• 5541
• 5655
• 5971
• 6210

Consider an amortization schedule for a loan at interest rate i per period, i > 0, being repaid with payments of 1 at the end of each period for n periods.

Determine which of the following statements about this schedule is true.

• The total interest paid equals [math]n-a_n[/math].
• The total interest paid equals [math]i a_n[/math].
• The total principal repaid equals [math]n-i a_n[/math].
• The principal repaid in payment [math]t[/math] equals [math]v^{n-t}[/math].
• The total payment amount equals [math]a_n[/math].