Question 1

Adel borrowed $6,500, 2 ½ years ago. She made a $800 payment 18 months ago. Using the financial functions on the calculator, determine how much she has to pay now if interest is 6.2% compounded monthly?

Accepted Answer

To solve this, we first calculate the future value of the initial loan after 2 ½ years (30 months) with monthly compounding interest, then subtract the future value of the payment made 18 months ago. Using the formula for future value $FV = PV(1 + r/n)^{nt}$, where $PV$ is the present value, $r$ is the annual interest rate, $n$ is the number of times the interest is compounded per year, and $t$ is the time the money is invested or borrowed for in years.1. Calculate the future value of the $6,500 loan after 2 ½ years:   - $PV = $6,500$   - $r = 6.2\% = 0.062$   - $n = 12$ (since interest is compounded monthly)   - $t = 2.5$ years   - $FV = $6,500(1 + 0.062/12)^{12*2.5}$2. Calculate the future value of the $800 payment made 18 months ago:   - $PV = $800$   - $t = 1$ year (since 18 months have passed and we're looking at the value 12 months from the payment)   - $FV = $800(1 + 0.062/12)^{12*1}$3. Subtract the future value of the payment from the future value of the loan to find out how much is owed now.Using a financial calculator or software to perform these calculations gives us the future value of the loan as more than the initial amount due to interest, and the future value of the payment as less than the future value of the loan. The correct answer, after performing these calculations and subtracting the future value of the payment from the future value of the loan, is $6,708.99.

Question 2

Debbie has two promissory notes payable to her. The first one will mature in five years at $42,371 and the second one will mature in eight years at $78,529. What amount can she expect to receive from the Lansky Finance Company if, one year from now, she sells both of the notes to them at a discount rate of 19% compounded annually?

Accepted Answer

The answer of Debbie has two promissory notes payable to...

Question 3

Twenty-five years ago Sandy invested $3,000. Fifteen years ago she put another $2,000 into the investment. Over the 25 years, interest has accumulated at a rate of 6% compounded monthly. How much interest has she earned over the 25 years?

Accepted Answer

To calculate the total interest earned, we need to calculate the future value of each investment separately and then sum them up, subtracting the initial investments to find the total interest earned. For the first investment of $3,000 made 25 years ago:- Using the formula for compound interest: A = P(1 + r/n)^(nt)- P = $3,000, r = 6% or 0.06, n = 12 (compounded monthly), t = 25- A = 3000(1 + 0.06/12)^(12*25) = 3000(1 + 0.005)^(300) ≈ $13,143.08For the second investment of $2,000 made 15 years ago:- P = $2,000, r = 6% or 0.06, n = 12, t = 15- A = 2000(1 + 0.06/12)^(12*15) = 2000(1 + 0.005)^(180) ≈ $5,160.16Total amount = $13,143.08 + $5,160.16 = $18,303.24Total interest earned = Total amount - Total initial investments = $18,303.24 - ($3,000 + $2,000) = $18,303.24 - $5,000 = $13,303.24The closest answer is E) $13,303, acknowledging a slight rounding difference in the final calculation.

Question 4

If Murphy puts $45,000 into an investment that earns 12% compounded monthly, and after three years he withdraws $30,000, how much money will the investment be worth seven years after the withdrawal?

Accepted Answer

First, calculate the value of the investment after three years using the formula for compound interest: A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount ($45,000), r is the annual interest rate (12%, or 0.12), n is the number of times that interest is compounded per year (12), and t is the time the money is invested for in years (3). This gives A = 45000(1 + 0.12/12)^(12*3) = $64,202. After withdrawing $30,000, the remaining amount is $34,202. Then, calculate the value of the remaining amount after seven more years using the same formula, which gives A = 34202(1 + 0.12/12)^(12*7) = $79,316.

Question 5

$3,500 borrowed one year ago, is to be settled by payments of $500 today, $1,500 six months from now, and a final payment eighteen months from now. What is the amount of the final payment if the interest rate on the loan is 12% compounded monthly?

Accepted Answer

To find the final payment, we need to calculate the present value of each payment and ensure they sum to the original loan amount. The interest rate is 12% compounded monthly, which is 1% per month. The present value of the $500 payment today is $500. The present value of the $1,500 payment six months from now is $1,500 / (1.01)^6. The final payment is made 18 months from now, so its present value is X / (1.01)^18. Setting the sum of these present values equal to $3,500 and solving for X gives the final payment amount.

Question 6

Doris is retiring today and she plans to buy a new car for $25,000 seven years from now and a second new car for $40,000 seventeen years from now. How much "new car money" should she set aside now if she can expect to earn 8½% compounded annually on her savings?

Accepted Answer

The answer of Doris is retiring today and she plans...

Question 7

A company borrowed $50,000 at 12% compounded monthly. It made a payment of $15,000 after two years, and $12,000 after three years. How much is required to pay off the loan one year after the second payment?

Accepted Answer

The answer of A company borrowed $50,000 at 12% compounded...

Question 8

Two payments of $7,500 each must be made three years and six years from now. If money can earn 8.4% compounded monthly, what single payment, four years from now, would be equivalent to the two scheduled payments?

Accepted Answer

The answer of Two payments of $7,500 each must be...

Question 9

Andy borrowed money four years ago at 13.2 % compounded monthly. He now owes a total of $13,743. How much of this is interest?

Accepted Answer

To find the interest, we need to calculate the principal amount first. Using the formula for compound interest: A = P(1 + r/n)^(nt), where A is the amount owed, P is the principal, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the time in years. Solving for P gives us the principal, and subtracting this from the total amount owed gives the interest. After calculations, the interest is $5,614.

Question 10

Nancy deposits $22,000 in an investment account earning 4.2% interest annually. In addition, she plans on withdrawing $4,000, $6,000 and $8,000 over a three-year period. Using the financial functions on the calculator, determine how much Nancy will have remaining at the end of year 3.

Accepted Answer

Nancy's account balance is calculated by considering the interest earned and the withdrawals made each year. After accounting for the interest and withdrawals over three years, the remaining balance is approximately $6,295.

Question 11

Eighteen years from now I will need to have $120,000 to pay for my child's post-secondary education. I anticipate being able to earn 14% compounded annually for the first 10 years and 11% compounded annually for years #11 through #20. What amount of money should I invest today in order to meet my goal?

Accepted Answer

To meet the goal of having $120,000 in 18 years with different interest rates for the periods, we need to calculate the present value of $120,000 discounted back 18 years using the given interest rates. For the last 8 years, the rate is 11% compounded annually. For the first 10 years, the rate is 14% compounded annually.First, calculate the present value of $120,000 after 8 years at 11%:$$ PV = \frac{FV}{(1 + r)^n} = \frac{120,000}{(1 + 0.11)^8} \approx 60,306.97 $$Then, calculate the present value of $60,306.97 (the amount needed in 10 years) at 14% for 10 years:$$ PV = \frac{60,306.97}{(1 + 0.14)^{10}} \approx 14,046 $$Therefore, an investment of approximately $14,046 today will grow to $120,000 in 18 years under the given conditions.

Question 12

Two payments of $850 and $600 must be made two years and five years from now respectively. If money can earn 4% compounded semi-annually, what single payment, three years from now, would be equivalent to the two scheduled payments?

Accepted Answer

The answer of Two payments of $850 and $600 must...

Question 13

A $10,000 eight-year investment earns interest at 12% compounded semi-annually. If it is sold 30 months before maturity to yield 16% compounded quarterly, what is its selling price?

Accepted Answer

First, calculate the future value of the investment at the original interest rate for the full term. Since the interest is compounded semi-annually, the number of compounding periods per year is 2, and the annual interest rate is 12%, which gives a period rate of 6%. The total number of periods is 8 years * 2 = 16 periods. Using the formula for compound interest, FV = P(1 + r)^n, where P is the principal, r is the rate per period, and n is the number of periods, we get FV = $10,000(1 + 0.06)^16 = $25,937.42.Next, calculate the present value of this future value 30 months (or 2.5 years) before maturity, with the new yield of 16% compounded quarterly. This gives 4 compounding periods per year, and with 2.5 years until maturity, there are 10 periods. The quarterly rate is 16%/4 = 4%. Using the present value formula, PV = FV / (1 + r)^n, we get PV = $25,937.42 / (1 + 0.04)^10 = $17,161.71.

Question 14

A $7,000 non-interest-bearing promissory note is discounted at 10% compounded quarterly, two years before maturity. What are the proceeds from the sale of the note?

Accepted Answer

The answer of A $7,000 non-interest-bearing promissory note is discounted...

Question 15

Today is Almo's 20^th birthday and he has just received a large amount of money to sign a contract with a professional hockey team. He wants to put away enough money to make sure that on his 50^th birthday he will have $2,500,000. For the next ten years he is confident that his investments will earn 15% compounded annually and after that, 10% compounded annually. How much must he invest today?

Accepted Answer

The answer of Today is Almo's 20^th birthday and he...

Question 16

Jack invested $10,000 at 10% compounded annually for 35 years. Jill also invested $10,000 for 35 years but her interest rate was 11% compounded annually. How much MORE interest did Jill earn as compared to Jack?

Accepted Answer

The answer of Jack invested $10,000 at 10% compounded annually...

Question 17

Albert purchased Bonzo's car for $500 cash and a non-interest bearing promissory note for $2,000 payable in two years. How much money can Bonzo expect to receive for the note if he immediately sells it to Corleone Finance Company at a discount rate of 30% compounded monthly?

Accepted Answer

To determine the present value of the $2,000 note that Bonzo sells to Corleone Finance Company, we use the formula for the present value of a single future amount: $PV = \frac{FV}{(1 + r)^n}$, where PV is the present value, FV is the future value ($2,000), r is the monthly interest rate (30% annual rate compounded monthly gives a monthly rate of $30\% / 12 = 2.5\%$, or 0.025 as a decimal), and n is the total number of compounding periods (2 years * 12 months/year = 24 months).Substituting the values, we get:$$PV = \frac{2000}{(1 + 0.025)^{24}}$$$$PV = \frac{2000}{(1.025)^{24}}$$$$PV = \frac{2000}{1.8061}$$ (rounded off)$$PV = 1106$$ (rounded to the nearest dollar)Therefore, Bonzo can expect to receive $1,106 for the note if he sells it immediately to Corleone Finance Company.

Question 18

Assume money can earn 15% compounded semi-annually. Rank the following payments in order of the payee's first choice, second choice, and third choice, respectively: 10,000 paid today, $20,000 to be paid five years from today, or $13,500,000 to be paid fifty years from today.

Accepted Answer

The present value of each option needs to be calculated to determine the best choice. The $10,000 today is already at its present value. The present value of $20,000 in 5 years and $13,500,000 in 50 years, when discounted at a 15% annual rate compounded semi-annually, will show that the $10,000 today is most valuable, followed by the $13,500,000 in 50 years, and lastly the $20,000 in 5 years. This is because the large future value of $13,500,000, even discounted back 50 years, is still more valuable than the other options when considering the power of compound interest over such a long period.

Question 19

Amanda borrowed $1,500, $3,500 and $5,000 at the beginning of each year. The rate of interest was at 4.8% compounded monthly. Using the financial functions on the calculator, determine the value that must be repaid at the end of year 3.

Accepted Answer

The correct answer is A because the future value of the three loans at the end of year 3 is $10,829.10. This can be calculated using the FV function on a financial calculator. The formula is:FV(rate, nper, pmt, pv, type)where:rate is the annual interest rate (4.8%)nper is the number of periods (3 years * 12 months = 36 months)pmt is the monthly payment ($1,500 + $3,500 + $5,000 = $10,000)pv is the present value of the loans ($1,500 + $3,500 + $5,000 = $10,000)type is the payment type (0 for end of period, 1 for beginning of period)Plugging these values into the calculator, we get:FV(0.048/12, 36, 10000, 0, 1) = $10,829.10

Question 20

Fred borrowed money 18 months ago at 12% compounded semi-annually. He now owes a total of $5,450. How much of this is interest?

Accepted Answer

The interest can be calculated using the formula for compound interest: A = P(1 + r/n)^(nt), where A is the amount owed, P is the principal amount (initial investment), r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time the money is invested for in years. Here, A = $5,450, r = 12% or 0.12, n = 2 (since the interest is compounded semi-annually), and t = 1.5 years (18 months). Rearranging the formula to solve for P gives P = A / (1 + r/n)^(nt). Substituting the given values and solving for P gives the initial amount borrowed. The interest is then A - P. Calculating this gives an interest amount of approximately $874.07.

Quiz 8: Compound Interest: Future Value and Present Value