BUQU 1130 The Nominal Annual Rate of Interest
What is the maturity value of a 120 day, $800 promissory note with interest of %7 p.a An investment dealer purchased 364 day Treasury bills worth $100,000. They were bought 200 days before maturity to yield 4.11%. What did the investor pay for the T-bills What is the accumulated value of $600 invested today at 8% p.a. compounded semi- annually for 5 years and3 months
4- What is the present value of $ 7,500 due in 9 years if interest 6% p.a. compounded monthly How much was paid for a $ 2,000 non-interest bearing note discounted 3 years and 6 months before its due date at 8% compounded quarterly What is the nominal annual rate of interest compounded semi-annually if $ 700 accumulates to $ 1150 in 3 years7- What is the effective interest rate of 6.3% p.a compounded monthly
Chris saves $ 150 each month-end for 5 years. If interest is 6% compounded monthly, how much interest earned $450 loan payment was due 5 months ago, but didn’t get paid and another payment is to be made 3 months from now for $800. What one amount paid today would be equivalent to these amounts if interest is 8.5% p.a. compounded monthly Determine the proceeds of a promissory note for $4000 with interest at 5% p.a. compounded quarterly, issued September 1, 2009, due on June 1, 2015, and discounted on December 1, 2012 at 8% compounded monthly.
- On August 12, Scottie borrowed $20,000 at 10.5% on note requiring payment of principle and interest on demand. She paid $ 5000 on November 1, $6000 on December 15, and the balance on February 25. The rate interest on the loan was 10.5% How much did she pay on February 25if she missed the first 5 payments, hoe much would have to pay at the end of the 6thmonth to bring her payments up to date ?If she credit union demanded payment in full after 6 moths, how much would she need.
- Wendy has contributed $ 2000 per year for the last ten years into an RRSP deposit with her bank in London, ON. Interest earned by these deposits was 4% compounded semi-annually for the first three years and 5.5% compounded quarterly for the last seven years. Five years after the last deposit, she converted her RRSP into a registered retirement income fund. How much was to beginning balance in the RRIF if interest for those five years remained 5.5% compounded quarterly.
- Find the equated date at which a payment of $600 due four months ago and payment of $600 due today could be settled by a payment of $1250 if interest is 9% compounded monthly.
- An investor purchased a 91-day, $100,000 T-bill on its issue date for $99,362.85. After holding it for 42 days, she sold the T-bill for a yield of 2.72%. What was the original yield rate of the T-bill For what price was the T-bill sold.
- Jenny borrowed money from ABC Bank and agreed to repay the loan in blended monthly payments of 918.65 over a four-year period. Interest on the loan was 5% compounded monthly. How much did she borrow.
Answer:
) C/Y, P, Y = 1
N= (120/365)
1/Y = 7%
PV= $ 800
CPT FV = $817.99
2) The formula for yield is shown below.
Yield = [(Selling Price – Purchase Price)/Purchase Price] * 365/Holding period
Let the purchase price be X
4.11 = ((100000-X)/X)*365/200
Solving the above, we get X = $ 97,797.55
3) C/Y, P, Y = 2
N=10.5
1/Y = 8%
PV= $ 600
CPT FV = $905.74
4) Present Value = 7500/(1+(6%/12))108 = $4,376.5
5) FV of note = $ 2,000
Time to maturity = 3 years 6 months or 10.5 quarters
Interest rate = 8% p.a. or 2% per quarter
Amount paid for the note = 2000/(1.0210.5) = $ 1,624.53
6) Let the nominal annual rate of interest be X %
Amount = $ 1,150
Principal = $ 700
Time period = 3 years or 6 half years
1150 = 700*(1+(X%/2))6
Solving the above, we get X = 13.98%
7) Effective interest rate (%) = [(1+(6.3%/12))12 -1]*100 = 6.49%
8) The future value of the annuity can be determined using the following formula.
In the given case, P = $ 150, r= (6/12) = 0.5% per month, n = 5 years or 5*12 = 60 months
Hence, FV of these payments = 150*[(1.005)60-1]/0.005 = $ 10,465.5
Total amount deposited = 150*60 = $ 9,000
Hence, interest earned = 10,465.5 – 9,000 = $ 1,465.50
1) The present value of two amounts needs to be found here. One was due 5 months ago and other which is due three months from now.
Interest rate = 8.5% p.a. compounded monthly
Amount due in past
Amount due = $ 450
Time = 5 months
Present value = 450*(1+ (8.5%/12))5 = $ 466.16
Amount due in future
Amount due = $ 800
Time = 3 months
Present value = 800/(1+ (8.5%/12))3 = $783.24
Total payment in the present required to discharge both debts = 466.16 + 783.24 = $ 1,249.
2) Face value = $ 5,000
Interest = 5% of 5000 = $ 25 per annum
Considering quarterly compounding , the interest would be paid @ $6.25 per quarter
Market required rate = 8% p.a. compounded monthly
Interest rate for three month = (1+ (8%/12))3 -1 = 2.013%
The following payments would be discounted at the above rate to determine the current price as shown below.
Hence, the value would be $ 4,152.47 as on December 1, 2012.
3) a) Let the amount paid on 25th February be $ X
The present value of all the three payments discounted at the given rate of interest should lead to $20,000 which is the underlying amount borrowed.
$ 5,000 was paid on November 1
Time from date of borrowing = November 1 – August 12 = 81 days
$ 6,000 was paid on December 15
Time from date of borrowing = December 15 – August 12 = = 125 days
$ X was paid on February 25
Time from date of borrowing = February 25 – August 12 = 197 days
Hence, 20000 = (5000/1.105(81/365) + (6000/1.105(125/365) (X/1.105(197/365)
Solving the above, we get X = $ 9,826.7
- b) Amount to be paid in the 6thpayment = 20000*(1.105(184/365)) = $ 21,032.42
- c) Total amount to be given to credit union for full payment assuming no payment has been done before for the borrowing = 20000*(1.105(184/365)) = $ 21,032.42
1) The future value of the payments made into the RRSP deposits at the end of the 10 years is indicated as follows.
For the last five years, when no new money has been deposited, interest has been earned on the above amount at the rate of 5.5% p.a. compounded monthly.
Hence, beginning balance in RRIF = 27047.61*(1+ (5.5%/4))20 = $ 35,542.35
2) Total payment made = $ 1,250
Debt due today = $ 600
For the debt of $ 600 which was due four months ago, the amount due would be = 600*(1+(9%/12))4 = $ 618.20
Hence, total debt due in today terms = 600 + 618.20 = $ 1,218.20
For settling, the above debt a payment of $ 1,250 has been made and hence the date would be in future.
1250 = 1218.20*(1+(9%/12))T
Solving the above, we get T = 3.56 months or 3 months 17 days
Hence the equated date would be 3 months 17 days from today.
3) The formula for yield is shown below.
Yield = [(Selling Price – Purchase Price)/Purchase Price] * 365/Holding period
- a) Original yield of T bill = [(100000 – 99362.85)/99,362.85]*(365/91) = 2.57%
- b) Yield earned during holding period is 2.72%
Hence, 2.72% = (Selling price - 99362.85)/99,362.85]*(365/42)
Solving the above, we get selling price = $130,462.1
4) The formula for installation is as indicated below.
EMI = P*R*(1+R)N/((1+R)N -1)
EMI = $918.65
Interest = 5% p.a. or (5/12) % or 0.41667% per month
N= 4 years or 48 months
918.65 = P*0.0041667*(1.0041667)48/(1.004166748-1)
Solving the above, we get P = $ 39,890.5
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