Math16269 Review for Final 2022
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Math 16269 – Review for Final
Chapter 9: Compound Interest Applications
1.
What single payment in 9 months would be equivalent to a payment of $900 due today and a payment of $1,200 due in 27 months if the interest rate is 4.2% compounded monthly? (Ans: $2,055.61)
2.
You had an agreement to pay $4,075 in 2 years from now and $6,725 in 5 years from now. What single payment would pay off this debt in one year from now if money earns 7.1% compounded quarterly? (Ans: $8,873.05)
3.
Payments on a debt were originally scheduled as follows: $500 in 9 months from today, $600 in 15 months from today, and $800 in 21 months from today. What is the
equivalent payment 15 months from today if interest is 5.3% compounded quarterly? (Ans: $1,892.55)
4.
Asia had an agreement to pay Sarbjit payments of $2,500 in 1 year from now and $3,000 in 30 months from now. How much should Asia pay Sarbjit 2 years from now in
order to clear the debt? Assume interest is 4% compounded quarterly. (Ans: $5,542.40)
5.
Ataina deposits $14,800 into an investment today that earns 5.5% compounded semi-
annually and maturing in 5 years. Suffy will wait until 6 months from today to make an investment that earns 6.1% compounded annually and maturing at the same time as Ataina's investment. a) How much will Ataina have in 5 years from today? (Ans: 19,412.44)
b) How much must Suffy invest in 6 months in order to have the same maturity value as Ataina? (Ans: 14,871.71)
6.
Expressed in years and months, how long will it take for $5,000, invested at 6% compounded monthly, to grow to $15,000? (Ans: 18 years, 5 months)
7.
In how many years will money quadruple at 8% compounded quarterly? (Ans: 17.5 years)
8.
A loan of $2,500 was repaid together with interest of $780. If interest was 7.1% compounded quarterly, for how many years and months was the money invested? (Ans: 3 years, 11 months)
9.
What monthly compounded rate is equivalent to 5.75% compounded semi-annually? (Ans: 5.68%)
10.
What is the effective rate corresponding to 7.2% compounded quarterly? (Ans: 7.4%)
11.
What is the semi-annually compounded rate that is the same as an effective rate of 18.5%? (Ans: 17.72%)
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12.
Which interest rate would you prefer to receive on a 3-year GIC: 6% compounded monthly, 6.1% compounded quarterly, or 6.2% compounded semi-annually? (Ans: 6.2% semi-annually)
13.
A department store credit card quotes a rate of 1.82% per month on any unpaid balances. What is the yearly effective rate of interest being charged? (Ans: 24.16%)
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Chapter 11: Annuities – Sections 11.1 to 11.3
14.
To finance a vacation in four years, Bernadette saves $530 at the beginning of every three months in an account paying interest at 3.92% compounded quarterly.
a.
What will be the balance in her account when she takes the vacation? (Ans: $9,222.21)
b.
How much of the balance will be interest? (Ans: $742.21)
c.
If she waits an additional year to start her vacation, and continues to save the same amount of money, how much more money will she have for her trip? ($2,539.32 more)
15.
Leo made deposits of $25 at the end of every month for 10 years in a savings account paying 3.5% compounded monthly. He plans on leaving his savings in the account for another 5 years. Assuming that the interest rate in his savings account is fixed during the entire time period, a.
How much would Leo have in his account at the end of the 15 years? (Ans: $4,270.50)
b.
How much would Leo have actually contributed to his savings over the 15 years? (Ans: $3,000)
c.
What would be the total interest earned on this investment? (Ans: $1,270.50)
16.
Sandu intends to contribute $2,500 to his RRSP every six months, starting today, and continuing for a total of 20 years. If the RRSP earns 8% compounded semi-
annually for the first seven years and 7% compounded semi-annually for the last 13 years, what amount will he have in the plan 20 years from now? (Ans: $223,224.92)
17.
A $5,000 bond pays $200 interest every quarter until the face value of the bond ($5,000) is repaid at maturity. What is the fair market value of the bond today if interest is 4.95% compounded semi-annually and the bond matures in 10 years? (Ans:
$9,355.13)
18.
Dina bought a dining set on a contract that requires monthly payments of $62.25 for three years. The first payment is made on the date of signing and interest is 24% compounded monthly. a.
What was the purchase price of the dining set? (Ans: $1,618.41)
b.
How much will Dina pay in total by the end of the three years? (Ans: $2,241)
c.
How much of what she pays will be interest? (Ans: $622.59)
19.
Raj just turned 43 and has already accumulated $34,500 in his RRSP. He makes additional month-end contributions of $300 to the plan and intends to do so until age 60. He plans to retire then and cease further contributions. The RRSP will be allowed to continue to accumulate earnings until he reaches age 65. The RRSP earns 4.2% compounded semi-annually.
a) What amount will his RRSP contain when he reaches age 65? (Ans: $195,407.84)
b) After he reaches age 65, Raj will withdraw money for 5 years. What start-of-year withdrawals can he make? (Ans: $42,396.00)
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20.
A new owner purchased a condominium unit by contracting to make annual payments of $21,300 for eight years. If the first payment is due on the date of purchase and interest is 3.98% compounded quarterly, what is the purchase price of the property? (Ans: $148,955.96)
21.
Sienna wants to buy a cottage but can afford to pay only $833.33 at the end of every month for the mortgage of 2.9% compounded semi-annually for the next 20 years. If she has $10,000 for the down payment, calculate the value of a cottage she can afford, her total investment, and interest paid over the mortgage period. (Ans: $161,862.27; $209,999.20; $48,136.93)
22.
What is the fair market value for a retirement annuity that would provide $3000 at the end of each month at 5% compounded quarterly for the first 10 years and $3000 at the end of each month at 6% compounded quarterly for the following 5 years? (Ans: $377,593.07)
23.
You want to invest in 15-year annuity that will pay you $3,600 per quarter for the first 7 years and $2,500 per month for the last 8 years. If the annuity earns 8.5% compounded annually for the first 7 years and 7.5% compounded semi-annually for the remaining 8 years, what would be the amount of your initial investment? (Ans: $178,163.02)
24.
The required monthly payment on a four-year loan bearing interest at 4% compounded monthly is $389.10.
a.
What was the original principal amount of the loan? (Ans: $17,232.79;)
b.
What is the balance owed just after the 27
th
payment? (Ans: $7,879.00)
c.
In total, how much interest was paid out if the balance owed was paid after the 27
th
payment? (Ans: $1,151.91)
25.
Loan payments of $600 at the beginning of each month were being made towards a brand new luxury car for a term of 5 years at 3.9% compounded annually. a.
Calculate the purchase price of the car if a down payment of $1000 was also required at the time of purchase. (Ans: $33,818.43 )
b.
How much will have been contributed towards paying off the loan by the end of the 5 years? How much of this is interest? (Ans: $37,000; $3,181.57)
c.
What is the balance owing on the loan after the 48
th
payment? How much interest is paid out, in total, if the balance owed is paid after the 48
th
payment? (Ans: $7,075.28; $3,056.85)
26.
Elijah already has $25,000 today in his savings account earning 3.5% compounded
semi-annually. The account will receive automatic month-end deposits of $275 for the
next 10 years. In 2 years from now, Elijah will withdraw $5,000 for a big anniversary party. a) How much will be in the account after the withdrawal 2 years from now? ($28,620.99)
b) How much will be in the account in 10 years from now? ($68,161.66)
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27.
An investment will pay you $50 at the end of every six months for 17 years. At the end of the 17 years, the investment will pay you an additional $1,000 along with the last regular $50 payment. What is the fair market value of the investment if the prevailing rate of return on similar investments is 4.5% compounded semi-annually? (Ans: $1,648.64)
28.
You want to buy a new flat screen television and have found pricing information from two major retailers:
a.
A: Pay $162.50 at the end of each month for the next 12 months.
b.
B: $500 today and an additional $72.50 at the end of each month for the next 18 months.
Which alternative is economically preferable if money is worth 6% compounded quarterly? In current dollars, how much will you save by selecting the preferred alternative?
(Ans: Retailer A=$1,888.38; Retailer B=$1,745.31; Retailer B offer is better by $143.07)
29.
The winner of a grand prize in a lottery can choose either $1,000,000 per year for 25 years or a single cash payment of $17,000,000 today. Which option should be chosen if payments are made at the beginning of each year and money can earn 3.2% compounded semi-annually? In today’s dollars, what is the economic advantage of the preferred choice? (Ans: Option 1 is better by $531,218.55)
Chapter 11: Annuities – Sections 11.4 to 11.6
30.
A contract can be fulfilled by making an immediate payment of $7,500 or equal payments at the end of every 6 months for 10 years. What is the size of the semi-
annual payments at 9.6% compounded semi-annually? (Ans: $591.66)
31.
How much does a depositor have to save at the end of every three months for seven years to accumulate $3,500 if interest is 3.75% compounded quarterly? (Ans: $109.89)
32.
Ruben bought a boat valued at $16,500 on an installment plan requiring a $2,000 down payment and equal end-of-month payments for five years. If interest is 7.5% compounded monthly, what is the size of the monthly payment? (Ans: $290.55)
33.
A vacation property valued at $125,000 was bought for 12 payments of $12,000 due at the beginning of every 6 months. What nominal annual rate of interest was charged? (Ans: 5.44%)
34.
If you save $75 at the beginning of every month for 10 years, for how long can you
withdraw $260 at the beginning of each month, starting 10 years from now, assuming
the interest is 6% compounded quarterly? Express your answer in years and months. (Ans: 4 years, 6 months)
35.
If contributions of $350 made into an RRSP at the beginning of every 3 months amounted to $15,449 after 8 years, what monthly compounded nominal rate of Page 5 of 7
interest was used? What would be the effective rate? (Ans: 7.46%; 7.72%)
36.
If Gerhart accumulated $5,700 in his savings account over five years, how much did he deposit at the beginning of every month if interest is 4.32% compounded monthly? (Ans: $84.97)
37.
a) For how long will Samir need to make payments of $500 at the end of every six months to save a total of $7,000 if interest is 2.25% compounded quarterly? Express your answer in years and months rounded up. (Ans: 6 years, 7 months)
b) How long would it take Samir to reach $7,000 if the initial balance was $3,000? (Ans: 3 years, 8 months)
38.
Thalani borrowed $10,000 to help finance her education. She intends to repay the loan with month-end payments of $350. If interest is 4% compounded quarterly, for how long will Thalani have to make monthly payments? Express your answer in years and months. (Ans: 2 years, 7 months)
39.
Rihannah placed earnings of $6,783 into a savings account. If she withdraws $575 at the end of each month, how long will the money last if interest is 3.15% compounded monthly? (Ans: 1 year)
40.
RRSP contributions of $4,345.11 at the end of every six months are projected to grow to be worth $400,000 in 25 years. What effective rate of interest was used for this forecast? (Ans: 4.65%)
41.
After 10.5 years of contributions of $2,000 at the end of every six months to an RESP, the accumulated amount stood at $65,727.82. What semi-annually compounded nominal rate of return was earned by the funds in the RESP? (Ans: 8.5%)
42.
Jatinder’s family wants to save $5000 to finance a vacation. They are able to save $240 at the beginning of each month, earning interest of 5% compounded monthly. In
years and months, how long will it take them to save enough money to take the trip? (Ans: 1 year, 8 months)
Special Application of Annuities – Leases (Section 12.4)
43.
Payments on a five-year lease valued at $48,750 are to be made at the beginning of every six months. If interest is 8.5% compounded quarterly, what is the size of the semi-annual payments? (Ans: $5,847.89)
44.
What is the cash value today of a three-year lease of office facilities renting for $735.50 payable at the beginning of each month if money is worth 6% compounded monthly? (Ans: $24,297.52)
45.
The marketing manager for Infiniti places an advertisement for the new Infiniti QX56. Suppose the MSRP of the vehicle is $75,050 with a residual value after 48 months of $29,602. What monthly lease payment should she advertise if a $5,000 Page 6 of 7
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down payment is required and Infiniti Financial Services requires 5.9% compounded annually on all leases? (Ans: $1,081.79)
46.
After taxes and applicable fees, a small service vehicle has a lease price of $39,544.35. If a $3,000 down payment is required, monthly payments are $680.37, what is the residual value of the vehicle after 3 years? Interest charged is 3.75% compounded annually. (Ans: $14,874.88)
47.
Proctor & Gamble plans to obtain production equipment for a lease price of $85,000 and requires a down payment of $15,000. What is the residual value after one year if interest charged is 9.99% compounded monthly and monthly payments are $5,609.67? (Ans: $6,250.03)
48.
Anderson is the production manager at Voortman Cookies. He is considering leasing a new high efficiency oven that will improve productivity. The terms of the 10-
year lease require quarterly payments of $35,125 including interest at 6.99% compounded monthly. a.
If the equipment is valued at $1,315,557.95 today, what is the estimated residual value of the equipment when the lease expires? (Ans: $592,137.21)
b.
If 4-year financing at 7.12% compounded quarterly is required to pay off the residual value of the lease, what end-of quarter payments must be made? (Ans: $42,854.63)
49.
A luxury vehicle can be purchased for $39,779.99 or leased for monthly payments of $485.50 for 5 years, with a down payment of $5,000 and a buy-back (residual value) of $12,450. If interest is 3.9% compounded annually, which option is preferred?
What is the economic advantage of the preferred choice? (purchase; E.A.= $2,057.92)
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