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Business Math Homework 4 Carolyn
Crosswell, who banks in New Jersey, wants to balance her checkbook,
which shows
a balance of $985.20.
The bank shows a balance of $1,430.33. The following transactions occurred: $135.20 automatic withdrawal to the gas company, $6.50 ATM fee, $8.00 service fee, and $1,030.05 direct deposit from the IRS. Carolyn used her debit card five times and was charged 45 cents for each transaction; she was also charged $3.50 for check printing. A $931.08 deposit was not shown on her bank statement. The following checks were outstanding: No. 235, $158.20 No. 237, $184.13 No. 238, $118.12 No. 239, $38.83. Carolyn received $2.33 interest. Carolyn's checkbook balance: $985.20 + IRS refund: $1,030.05 + Interest: $2.33 Total in add: $1,032.38 Balance + Total: $2,017.58 - ATM fee: ($6.50) - Service fee: ($8.00) - Gas Company: ($135.20) - Printing: ($3.50) - Debit: ($2.25) Total in Deduct: $155.45 Reconciled Balance: = $1,862.13 Carolyn's Bank balance: $1,430.33 + Deposit in transit: $931.08 Balance + DIT= $2,361.41 - Outstanding checks (total) ($499.28) Reconciled Balance: = $1,862.13 Melissa Jackson, bookkeeper for Kinko Company, cannot prepare a bank reconciliation. The bank statement showed a $2,955.82 balance. Melissa's checkbook showed a $3,301.82 balance. Melissa placed a $510.19 deposit in the bank's night depository on June 30, 2015. The deposit did not appear on the bank statement. The bank included two DMs and one CM with the returned checks: $690.65 DM for NSF check, $8.50 DM for service charges, and $400.00 CM (less $10 collection fee) for collecting a $400.00 non-interest-bearing note. Check No. 811 for $110.94 and check No. 912 for $82.50, both written and recorded on June 28, were not with the returned checks. The bookkeeper had correctly written check No. 884, $1,000, for a new cash register, but she recorded the check as $1,069. The May bank reconciliation showed check No. 748 for $210.90 and check No. 710 for $195.80 outstanding on April 30. The June bank statement included check No. 710 but not check No. 748. Kinko's checkbook balance: $3,301.82 + Collection on notes receivable: $400.00 - Collection fee: ($10.00) Notes-fee $390.00 Error in recording: $69.00 Balance + (Notes-fee) + Error $3,760.82 - NSF Check: ($690.65) - Service Charge: ($8.50) Total in deduct: $699.15 Reconciled Balance: $3,061.67 Kinko's bank balance: $2,955.82 + Deposit in transit: $510.19 Balance + DIT $3,466.01 - Outstanding checks (total): ($404.34) Reconciled balance: $3,061.67 Using the check register below and the following bank statement, prepare a bank reconciliation for Lee.com. Lee.com checkbook balance: $4,720.33 - Service charge ($15.00) Ending Checkbook balance: $4,705.33 Lee.com bank balance: $4,823.01 + Deposit in transit: $400.30 - Outstanding checks (total): ($517.98) Ending bank balance: $4,705.33 Fill out the check register that follows with this information: 2015 July 7: No. 959 AT+T $143.50 July 15: No. 960 Staples 66.10 July 19 Deposit 800.00 July: 20 No. 961 West Electric 451.88 July: 24 No. 962 Bank of America 319.24 July: 29 Deposit 400.30 Balance: $44,500.75 959 7/7 AT + T $ 143.50 - 143.50 = 4,357.25 960 7/15 Staples 66.10 -66.10 = 4,291.15 7/19 Deposit 800.00 800.00 = 5,091.15 961 7/20 West Electric 451.88 - 451.88 = 4,639.27 962 7/24 Bank of America 319.24 - 319.24 = 4,320.03 7/29 Deposit 400.30 400.30 Balance: $4,720.33 The World Bank forecasts growth of world trade to be 3%, up from 2.6% in 2014. This change has caused Galapagos Islands Resort to analyze its current financial situation, beginning with reconciling its accounts. Galapagos Islands Resort received its bank statement showing a balance of $8,788. Its checkbook balance is $15,252. Deposits in transit are $3,450 and $6,521. There is a service charge of $45 and interest earned of $3. Notes collected total $1,575. Outstanding checks are No. 1021 for $1,260 and No. 1022 for $714. All numbers are in U.S. dollars. Galapagos Islands Resort checkbook balance: $ 15,252.00 + Notes collected: $1,575 + Interest earned: $3.00 Total in add: $1,578.00 Balance + Total $16,830.00 - Service charge: ($45) Reconciled balance: $16,785.00 Galapagos Islands Resort bank balance: $8,788.00 + Deposit in transit (total): $9,971.00 Balance + DIT = $18,759.00 - Outstanding checks (total): ($1,974.00) Reconciled balance: $16,785.00 A local bank began charging $2.50 each month for returning canceled checks. The bank also has an $8.00 "maintenance" fee if a checking account slips below $750. Donna Sands likes to have copies of her canceled checks for preparing her income tax returns. She has received her bank statement with a balance of $535.85. Donna received $2.68 in interest and has been charged for the canceled checks and the maintenance fee. The following checks were outstanding: No. 94, $121.16; No. 96, $106.30; No. 98, $210.12; No. 99, $64.84. A deposit of $765.69 was not recorded on Donna's bank statement. Her checkbook shows a balance of $806.94. Donna's checkbook balance: $806.94 + Interest: $2.68 Balance + interest $809.62 - Canceled check: ($2.50) - Maintenance fee: ($8.00) Total deduct: $10.50 Reconciled balance: $799.12 Donna's bank balance: $535.85 + Deposit in transit: $765.69 Balance + DIT $1,301.54 - Outstanding checks (total) ($502.42) Reconciled balance: $799.12 Kameron Gibson's bank statement showed a balance of $717.72. Kameron's checkbook had a balance of $209.50. Check No. 104 for $110.07 and check No. 105 for $15.55 were outstanding. A $620.50 deposit was not on the statement. He has his payroll check electronically deposited to his checking account the payroll check was for $1,025.10. There was also a $4 teller fee and an $18 service charge. Kameron's checkbook balance: $209.50 + Direct deposit: $1,025.10 Balance + deposit $1,234.60 - teller fee: ($4.00) - Service charges: ($18.00) Total deduct: ($22.00) Reconciled balance: $1,212.60 Kameron's bank balance: $717.72 +Deposit in transit: $620.50 Balance + DIT $1,338.22 - Outstanding checks (total): ($125.62) Reconciled balance: $1,212.60 Banks are finding more ways to charge fees, such as a $25 overdraft fee. Sue McVickers has an account in Fayetteville; she has received her bank statement with this $25 charge. Also, she was charged a $6.50 service fee; however, the good news is she earned $5.15 interest. Her bank statement's balance was $315.65, but it did not show the $1,215.15 deposit she had made. Sue's checkbook balance shows $604.30. The following checks have not cleared: No. 250, $603.15; No. 253, $218.90; and No. 254, $130.80. Sue's Checkbook balance: $604.30 +Interest: $5.15 Balance + Interest $609.45 - Overdraft: ($25.00) - Service charge: ($6.50) Total deduct: $31.50 Reconciled balance: $577.95 Sue's bank balance: $315.65 +Deposit in transit: $1,215.15 Balance + DIT $1.530.80 - Outstanding checks (total): ($952.85) Reconciled balance: $577.95 Lowell Bank reported the following checking account fees: $2 to see a real-live teller, $20 to process a bounced check, and $1 to $3 if you need an original check to prove you paid a bill or made a charitable contribution. This past month you had to transact business through a teller six times—a total $12 cost to you. Your bank statement shows a $305.33 balance; your checkbook shows a $1,009.76 balance. You received $1.10 in interest. An $801.15 deposit was not recorded on your statement. The following checks were outstanding: No. 413, $28.30; No. 414, $18.60; and No. 418, $60.72. Checkbook balance: $1,009.76 + Interest: + $1.10 Balance + Interest $1,010.86 - Teller fee: - $12.00 Reconciled balance: $998.86 Bank balance: $305.33 +Deposit in transit: + $801.15 Balance + DIT $1,106.48 - Outstanding checks (total): - $107.62 Reconciled balance: $998.86
Complete the
following table, assuming
an interest rate of 10% compounded quarterly.
Make a table
with the same headings as previous, but for a loan of
$12,000 for 5 months at 15% compounded monthly.
Write the following nominal rates in the “jm” notation and find the corresponding periodic rates, i (include the period with these). The first line is completed as an example.
Write each of the following rates as nominal rates and complete the table.
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Government compound-interest savings bonds have the interest compounded every year. Suppose that a $1,000 bond paid interest at 8.5% compounded annually and was kept for three years. Find the value (Future Value) of the bond at the end of the three years by: Showing the interest and balance each year. Using the compound-interest formula to get FV at the end of two years. Year Interest Balances 0 $1,000.00 1 $85.00 $1,085.00 2 $92.23 $1,177.23 3 $100.06 $1,277.29 A loan of $24,000 for two years is to carry interest at 14% compounded semi-annually. Use the compound-interest formula to find the value of the loan at the end of two years. $31,459.10 A “junk” bond was supposed to pay interest at 25% paid annually. Unfortunately, no payments were made for the last seven years, so the interest was allowed to compound at 25% compounded annually. Find the value at the end of each of the seven years for a bond with a principal of $1,000 at the start. Also find the value the loan would have had at the end of each year if the interest had been simple interest at 25% annually. Note the difference caused by compounding. Year Balance 0 $1,000.00 1 $1,250.00 2 $1,562.50 3 $1,953.13 4 $2,441.41 5 $3,051.76 6 $3,814.70 7 $4,768.38 Year Balance 0 $1,000.00 1 $1,250.00 2 $1,500.00 3 $1,750.00 4 $2,000.00 5 $2,250.00 6 $2,500.00 7 $2,750.00 Find the present values of each of the amounts below, filling in the rest of the table when you do so. Check your last result by assuming the PV was invested for one year in an account paying 10% compounded quarterly and adding on the interest each period as in Problem 1.
PV Interest Rate Length n FV $11,500 6.5% compounded semi-annually 2 years 8 $11,364.76 $7,400 16% compounded monthly 3.5 years 4 $25,000.00 $14,000 I0% compounded quarterly 1 year 8 $30,000.00 According to the terms of his uncle’s will, Tom Jones is to receive $50,000 2.5 years from now. Tom would like to borrow as much as he can now and pay it off with his inheritance. Use the compound-interest formula to find out how much he can borrow if the interest rate is as follows: a. 10% compounded monthly. b. 9% compounded monthly. c. 8% compounded monthly. a. $38,980.40 b. $39,959.34 c. $40,963.72 Ann Lee has a lease on a government property which must be paid by a lump sum of $6,000 every year. The next payment is due in 10 months from now, and Ann plans to invest enough money in an account at her bank so that the amount in the account in 10 months will cover the $6,000 payment. If the interest rate is 8.5% compounded monthly, how much should she place in the account? $5,591.10 Ajax Company is borrowing $100,000 now and has agreed to pay 11% compounded annually on the outstanding balance at all times. Ajax plans to pay $30,000 at the end of the first year of the loan and $35,000 at the end of the second year. The remaining debt is to be completely paid off by a single payment at the end of the third year. Draw a cash-flow diagram and find the amount that should be paid at the end of the third year by: Finding the interest and balance due at the end of each year. Using an equation of value at a focal date (e.g., at year 3). Year Balance 1 $81,000.00 2 $54,910.00 3 $60,950.10 b. $100,000 (1.11)3 = $30,000 (1.11)2 + $35,000 (1.11) + x x = $60,950.10 AC Holdings has taken over a company with a debt that was to be paid by a payment of $85,000 one year from now. Instead, AC has agreed with the holder of the debt to pay it off early and be allowed 12% compounded quarterly for early payment. It plans to pay $40,000 now and the rest in six months. a. Draw a cash-flow diagram and find the amount that should be paid in 6 months. b. Repeat (a) but assume the payments now and in 6 months are to be equal in size. a. $37,684.65 b. $38,876.54 North Credit Union advertises that it will pay 7% compounded annually on money on deposit for periods longer than one year and that the money may be taken out, with interest, at any time after the first year. A depositor placed $20,000 on deposit at the above rate for four years, but decided to withdraw it after 2.5 years. How much should the depositor receive? Show that, if this amount were deposited at the same rate for the remaining 1.5 years, the result would be the same as if it had never been withdrawn. a. $23,685.88 b. FV = $ 23,685 (1.07)1.5 = $ 20,000(1.07)4 = $ 26,215.92 A loan of $17,000 for three years resulted in a future value of $21,560.11. Use your calculator functions to find the nominal interest rate if the loan was compounded: a. quarterly b. semi-annually. a. 8% compounded quarterly. b. 8.08% compounded semi-annually. Use your calculator functions to find the FV of a principal of $1.00 invested for one year at 16% compounded quarterly, and leave the results in your calculator. Then find the nominal monthly rate that will give the same FV – the rate compounded monthly that is equivalent to 16% compounded quarterly. Check your answer by finding the future value of a principal of $10,000 invested for two years at each rate. You should get the same answer in each case. 16% compounded quarterly = 15.7913% compounded monthly. Complete the following table of equivalent nominal rates, giving answers in percent to six decimals. Each row will contain equivalent rates.
Effective Rate, j1 j2 j4 j12 17.227080% 16.214281% 16.542910% 16% 12.550881% 12.180000% 12% 11.881961% 9.202500% 9% 8.900966% 8.835748% Use your results in Row 1 in the previous problem to find the future value of a loan of $4,000 for 18 months by doing the compounding: a. monthly. b. Quarterly. c. Semi-annually d. Annually
Your first
child was born
this year and you decide to save for her education.
You deposit $2,000 into an RESP (registered education savings plan) that pays 4.5% compounded annually (j1=0.045). How much will your child have in 18 years? Use both the formula and the TVM Keys. $4,416.96 You borrow $5,000 from a private loan company and agree to pay it back with interest calculated at 10% compounded quarterly. How much will you owe in 30 months? Use both the formula and the TVM Keys. $6,400.42 You are expecting a tax refund of $3,000 six months from now. You take your T4 slips to H&P Square Tax preparation service and they agree to give you the money now if you sign over the refund to them. How much money will you receive today if interest is calculated at j12 = 9$%. Use both the formula and the TVM Keys. $2,868.47 You go to purchase a brand new motorcycle and the dealer quotes you a price of $14,000 to be paid as a single payment in 30 months. You would like to pay cash today for the motorcycle. How much should you offer if interest is calculated at 8% compounded semi annually? Use the formula and the TVM Keys. $11,506.98 You have $75,000 and decide to purchase a 30 year Government of Canada strip bond with an interest rate of 7.0% compounded semi-annually. How much will the bond be worth in 30 years? (i.e., what is the maturity value of the strip bond?) $590,856.82 A. Financial planners predict you will need one million dollars to retire. You would like to buy a 30-year strip bond with an interest rate of 7% compounded semi-annually that has a maturity value of 1 million dollars. How much will you need to pay for this strip bond today? B. Unfortunately, you only have $75,000 available to buy a bond. You are considering buying a junk bond (risky bond) because you know that the interest rates are much. higher than for a Government of Canada bond. What nominal interest rate, compounded semi-annually, do you require so that the bond will have a maturity value of $1,000,000 in 30 years? C. Your friend convinces you that junk bonds are too risky to be used as a retirement investment. If instead, you buy the Government of Canada bond (with your $75,000) that pays 7% compounded semi-annually, how many years will it take you to reach your goal of having $1,000,000? A. $126,934.31 B. 8.82331% C. 37.65 years If an investment grows from $10,000 to $16,000 in 27 months, what was the nominal rate of interest, compounded quarterly? j4 = 21.44411% If an investment grows from $4,000 to $6,000 in 48 months, what was the nominal rate of interest: compounded monthly? compounded quarterly? compounded semi-annually? compounded annually? j12 = 10.17956% j4 = 10.26616% j2 = 10.39790% j1 = 10.66819% You would like to save to return to school. You deposit $4,000 into a GIC that pays . You have decided to return to school when your savings grows to at least $6,000. If you make no more contributions, how many years will it take you to reach your goal? 5.5 years How many years will it take $300.00 to accumulate to $425.29 at 7% compounded monthly? 5.0 years |
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