Question 1

Find the future value of the ordinary annuity. Interest is compounded annually, unless otherwise indicated:
-PMT = $7,500, i = 7% interest compounded semiannually for 4 years
A) $ 131,254.61
B) $ 58,345.56
C) $ 67,887.65
D) $ 282,173.37

Accepted Answer

The future value of an ordinary annuity can be calculated using the formula: $FV = PMT \times \frac{((1 + r)^n - 1)}{r}$, where PMT is the payment amount per period, r is the interest rate per period, and n is the total number of payments. Since the interest is compounded semiannually, the annual interest rate (7%) must be divided by 2, and the number of years (4) must be multiplied by 2, giving us an effective r of 0.035 and n of 8. Plugging these values into the formula gives us the future value of the annuity.

Question 2

Find the periodic payment that will render the sum:
-FV = $ 42,000, interest is 8% compounded monthly, payments made at the end of each month for 3 years
A) $ 3373.51
B) $ 1036.13
C) $ 2213.19
D) $ 12,433.54

Accepted Answer

To find the periodic payment (PMT) for a future value (FV) annuity, where payments are made at the end of each period, we use the Future Value of an Ordinary Annuity formula: $FV = PMT \times \frac{[(1 + r)^n - 1]}{r}$, where FV is the future value, PMT is the periodic payment, r is the monthly interest rate (annual rate divided by 12), and n is the total number of payments (months). Given: FV = $42,000, annual interest rate = 8% (or 0.08), compounded monthly, so monthly interest rate $r = \frac{0.08}{12}$, and the total number of payments over 3 years (n = 3 years × 12 months/year = 36 months). Rearranging the formula to solve for PMT gives us $PMT = FV \times \frac{r}{[(1 + r)^n - 1]}$. Substituting the given values and solving for PMT yields approximately $1036.13.

Question 3

Larry wants to start an IRA that will have $ 400,000 in it when he retires in 22 years. How much should he invest semiannually in his IRA to do this if the interest is 9% compounded semiannually?
A) $ 3019.28
B) $ 11,018.26
C) $ 3032.28
D) $ 2889.93

Accepted Answer

To solve this, we use the formula for the future value of an annuity: $FV = P \times \left(\frac{(1 + r)^n - 1}{r}\right)$, where $FV$ is the future value, $P$ is the payment per period, $r$ is the interest rate per period, and $n$ is the total number of payments. Here, $FV = \$400,000$, $r = \frac{0.09}{2} = 0.045$ (since the interest is compounded semiannually), and $n = 22 \times 2 = 44$ (because payments are made semiannually for 22 years). Rearranging the formula to solve for $P$ gives us $P = \frac{FV}{\left(\frac{(1 + r)^n - 1}{r}\right)}$. Plugging in the values, we get $P = \frac{400,000}{\left(\frac{(1 + 0.045)^{44} - 1}{0.045}\right)}$, which calculates to approximately \$3032.28.

Question 4

Cara needs $9,000 in 6 years. What amount can she deposit at the end of each quarter at 6% interest compounded quarterly so she will have her $9,000?
A) $ 1290.26
B) $ 299.37
C) $ 314.32
D) $ 330.58

Accepted Answer

To find the amount Cara needs to deposit each quarter, we use the future value of an ordinary annuity formula: FV = Pmt * [(1 + r)^nt - 1] / r. Here, FV = $9,000, r = 0.06/4 = 0.015, n = 4 quarters per year, t = 6 years. Solving for Pmt gives approximately $314.32.

Question 5

Find the rate of interest required to achieve the conditions set forth:
-A = $ 32,000
P = $8,000
T = 20 years
Compounded annually
A) 5.6467%
B) 8%
C) 3.5265%
D) 7.1773%

Accepted Answer

The answer of Find the rate of interest required to...

Question 6

Find the rate of interest required to achieve the conditions set forth:
-A = $ 32,000
P = $8,000
T = 20 years
Compounded quarterly
A) 3.4959%
B) 3.5489%
C) 5.5310%
D) 6.9919%

Accepted Answer

The answer of Find the rate of interest required to...

Question 7

Find the rate of interest required to achieve the conditions set forth:
-If Jay bought a lot for $8,000 and sold it 15 years later for $24,000, what was her percentage rate of return on this investment if it was compounded annually?
A) 9.6825%
B) 8.7104%
C) 3.7995%
D) 7.5990%

Accepted Answer

The answer of Find the rate of interest required to...

Question 8

Solve for the missing value. Round to four decimal places: -_n₌_{33; i}₌_{0.05; PMT}₌_{$1; PV}₌_? A) $ 15.8027 B) $ 16.0025 C) $ 16.1929 D) $ 23.9975

Accepted Answer

The answer of Solve for the missing value. Round to...

Question 9

Solve for the missing value. Round to four decimal places:
-n = 30; i = 0.03; PMT = $100; PV = ?
A) $2000.0441
B) $4706.6287
C) $1918.1585
D) $1960.0441

Accepted Answer

The answer of Solve for the missing value. Round to...

Question 10

Find the present value of the ordinary annuity:
-Payments of $ 65 made quarterly for 10 years at 8% compounded quarterly
A) $ 1789.81
B) $ 638.18
C) $ 1748.67
D) $ 1778.11

Accepted Answer

The answer of Find the present value of the ordinary...

Question 11

Find the payment necessary to amortize the loan:
-$ 12,200; 12% compounded monthly; 48 monthly payments
A) $ 321.27
B) $ 1470.38
C) $ 321.50
D) $ 316.16

Accepted Answer

The payment necessary to amortize the loan can be found using the loan amortization formula, which is P = [rPV] / [1 - (1 + r)^-n], where P is the payment, r is the monthly interest rate (annual rate divided by 12), PV is the present value of the loan, and n is the number of payments. Here, r = 0.12/12 = 0.01, PV = $12,200, and n = 48. Plugging these values into the formula gives a payment of approximately $321.27.

Question 12

Find the payment necessary to amortize the loan:
-$2200; 12% compounded quarterly; 8 quarterly payments
A) $313.40
B) $442.87
C) $313.64
D) $282.23

Accepted Answer

The correct answer is A because the payment necessary to amortize the loan is $313.40. This can be calculated using the formula for the present value of an annuity, which is:PV = PMT * [1 - (1 + r)^-n] / rwhere:PV is the present value of the annuityPMT is the payment amountr is the interest rate per periodn is the number of periodsIn this case, the present value of the loan is $2200, the interest rate is 12% compounded quarterly, and the number of periods is 8. Plugging these values into the formula, we get:$2200 = PMT * [1 - (1 + 0.03)^-8] / 0.03$2200 = PMT * [1 - 0.7441] / 0.03$2200 = PMT * 8.3333PMT = $2200 / 8.3333PMT = $313.40

Question 13

The monthly payments on a $73,000 loan at 13% annual interest are $807.38. How much of the first monthly payment will go toward the principal?
A) $702.42
B) $16.55
C) $790.83
D) $104.96

Accepted Answer

The answer of The monthly payments on a $73,000 loan...

Question 14

The monthly payments on a $79,000 loan at 14% annual interest are $982.76. How much of the first monthly payment will go toward interest?
A) $137.59
B) $845.17
C) $921.67
D) $1106.00

Accepted Answer

To calculate the interest portion of the first monthly payment, you multiply the total loan amount by the annual interest rate, and then divide by 12 (to get the monthly interest amount). For a $79,000 loan at 14% annual interest: ($79,000 * 0.14) / 12 = $921.67.

Question 15

Use an amortization table to solve the problem. Round to the nearest cent.
-The monthly payments on a $73,000 loan at 13% annual interest are $807.38. How much of the first monthly payment will go toward the principal?
A) $702.42
B) $790.83
C) $104.96
D) $16.55

Accepted Answer

The answer of Use an amortization table to solve the...

Question 16

Use an amortization table to solve the problem. Round to the nearest cent.
-The monthly payments on a $76,000 loan at 12% annual interest are $836.76. How much of the first monthly payment will go toward interest?
A) $100.41
B) $912.00
C) $736.35
D) $760.00

Accepted Answer

The interest for the first month is calculated on the initial loan amount. At 12% annual interest, the monthly interest rate is 1% (12% / 12 months). Therefore, the interest for the first month is 1% of $76,000, which is $760.

Question 17

Solve the problem. Assume no new purchases are made with the credit card.
-The annual interest rate on a credit card is 16.99%. If a payment of $100.00 is made each month, how long will it take to pay off an unpaid balance of $1746.42?
A) 15 months
B) 23 months
C) 21 months
D) 20 months

Accepted Answer

The correct answer is C.The monthly interest rate is 16.99% / 12 = 1.416%. The monthly payment is $100.00. The unpaid balance after the first month is $1746.42 * (1 + 0.01416) - $100.00 = $1652.67. The unpaid balance after the second month is $1652.67 * (1 + 0.01416) - $100.00 = $1560.62. The unpaid balance after the third month is $1560.62 * (1 + 0.01416) - $100.00 = $1470.27. The unpaid balance after the fourth month is $1470.27 * (1 + 0.01416) - $100.00 = $1381.62. The unpaid balance after the fifth month is $1381.62 * (1 + 0.01416) - $100.00 = $1294.67. The unpaid balance after the sixth month is $1294.67 * (1 + 0.01416) - $100.00 = $1209.42. The unpaid balance after the seventh month is $1209.42 * (1 + 0.01416) - $100.00 = $1125.87. The unpaid balance after the eighth month is $1125.87 * (1 + 0.01416) - $100.00 = $1043.92. The unpaid balance after the ninth month is $1043.92 * (1 + 0.01416) - $100.00 = $963.57. The unpaid balance after the tenth month is $963.57 * (1 + 0.01416) - $100.00 = $884.82. The unpaid balance after the eleventh month is $884.82 * (1 + 0.01416) - $100.00 = $807.67. The unpaid balance after the twelfth month is $807.67 * (1 + 0.01416) - $100.00 = $732.12. The unpaid balance after the thirteenth month is $732.12 * (1 + 0.01416) - $100.00 = $658.17. The unpaid balance after the fourteenth month is $658.17 * (1 + 0.01416) - $100.00 = $585.82. The unpaid balance after the fifteenth month is $585.82 * (1 + 0.01416) - $100.00 = $515.07. The unpaid balance after the sixteenth month is $515.07 * (1 + 0.01416) - $100.00 = $445.92. The unpaid balance after the seventeenth month is $445.92 * (1 + 0.01416) - $100.00 = $378.37. The unpaid balance after the eighteenth month is $378.37 * (1 + 0.01416) - $100.00 = $312.42. The unpaid balance after the nineteenth month is $312.42 * (1 + 0.01416) - $100.00 = $248.07. The unpaid balance after the twentieth month is $248.07 * (1 + 0.01416) - $100.00 = $185.32. The unpaid balance after the twenty-first month is $185.32 * (1 + 0.01416) - $100.00 = $124.17. The unpaid balance after the twenty-second month is $124.17 * (1 + 0.01416) - $100.00 = $64.62. The unpaid balance after the twenty-third month is $64.62 * (1 + 0.01416) - $100.00 = $4.77. The unpaid balance after the twenty-fourth month is $4.77 * (1 + 0.01416) - $100.00 = -$90.58. Therefore, it will take 21 months to pay off the unpaid balance of $1746.42.

Quiz 3: Mathematics of Finance

Find the future value of the ordinary annuity. Interest is compounded annually, unless otherwise indicated: -PMT = $7,500, i = 7% interest compounded semiannually for 4 years

Find the periodic payment that will render the sum: -FV = $ 42,000, interest is 8% compounded monthly, payments made at the end of each month for 3 years

Larry wants to start an IRA that will have $ 400,000 in it when he retires in 22 years. How much should he invest semiannually in his IRA to do this if the interest is 9% compounded semiannually?

Cara needs $9,000 in 6 years. What amount can she deposit at the end of each quarter at 6% interest compounded quarterly so she will have her $9,000?

Find the rate of interest required to achieve the conditions set forth: -A = $ 32,000 P = $8,000 T = 20 years Compounded annually

Find the rate of interest required to achieve the conditions set forth: -A = $ 32,000 P = $8,000 T = 20 years Compounded quarterly

Find the rate of interest required to achieve the conditions set forth: -If Jay bought a lot for $8,000 and sold it 15 years later for $24,000, what was her percentage rate of return on this investment if it was compounded annually?

Solve for the missing value. Round to four decimal places: -n = 33; i = 0.05; PMT = $1; PV = ?

Solve for the missing value. Round to four decimal places: -n = 30; i = 0.03; PMT = $100; PV = ?

Find the present value of the ordinary annuity: -Payments of $ 65 made quarterly for 10 years at 8% compounded quarterly

Find the payment necessary to amortize the loan: -$ 12,200; 12% compounded monthly; 48 monthly payments

Find the payment necessary to amortize the loan: -$2200; 12% compounded quarterly; 8 quarterly payments

The monthly payments on a $73,000 loan at 13% annual interest are $807.38. How much of the first monthly payment will go toward the principal?

The monthly payments on a $79,000 loan at 14% annual interest are $982.76. How much of the first monthly payment will go toward interest?

Use an amortization table to solve the problem. Round to the nearest cent. -The monthly payments on a $73,000 loan at 13% annual interest are $807.38. How much of the first monthly payment will go toward the principal?

Use an amortization table to solve the problem. Round to the nearest cent. -The monthly payments on a $76,000 loan at 12% annual interest are $836.76. How much of the first monthly payment will go toward interest?

Solve the problem. Assume no new purchases are made with the credit card. -The annual interest rate on a credit card is 16.99%. If a payment of $100.00 is made each month, how long will it take to pay off an unpaid balance of $1746.42?

Solve for the missing value. Round to four decimal places: -_n₌_{33; i}₌_{0.05; PMT}₌_{$1; PV}₌_?