Question

1. Cecilia’s grandfather set up a savings account for her with a $25,000 gift when she was born. The account accumulated interest annually at a rate of 6% per year and no other deposits were made to the account. Cecilia is 21 years old today. To date, how much has accumulated in the account?
2. Wade’s company needs to have a lump-sum deposit of $200,000 for the purchase of a piece of equipment in 2 years. He wishes to deposit a sum of cash into an account paying 4% per year compounded on a monthly basis. How much will he need to deposit into this account to have enough to purchase the equipment?
3. Julie and Miguel just got married and are planning on an anniversary cruise for their fifth year anniversary. They estimate the trip will cost $10,000. How much should they deposit to have enough(in 5 years)in savings to pay for the cruise, assuming a 4% interest rate annually?
4. You know you will receive a $12,000 bonus each year for the next three years. You plan to save it for your first home down payment. How much will you have in the account at the end of 3 years if you earned 3% annually?
5. Santiago plans to save for a vacation to Brazil in 1.5 years. He will be putting the money into a short-term investment account earning 4% compounded monthly. How much will Santiago have to put away at the beginning of each month if the total package cost for the trip is $3,500?
6. Margaret purchased a collection of stamps for $6,500. Today she sold the stamps for $12,600. Margaret estimated her average opportunity cost on the stamps was 12.5% (compounded monthly). Approximately how many years did she own the stamps?
7. Three years ago, Brian borrowed $1,800 from his parents to pay off his credit card debt. Brian won the lottery and decided to pay his parents back a total of $2,500. What is the average interest rate of the loan from Brian’s parents?
8. Carol just purchased a home for $400,000 and paid 30% as a down payment? She financed the balance over 30 years at 4.75%. She makes monthly payments. What are the payments? How much interest will she pay over the life of the loan?
9. You need to accumulate $1,000 in 5 years. If you can afford to invest $150 at the end of each year, what rate of return will be required to reach your goal?
10. You want to purchase a $23,000 car when you graduate in 3 years. You just received a substantial inheritance of $15,000 and want to put it in an account that earns 8% annually to purchase the car in 3 years. Will you have enough to cover the cost of the car when you graduate? If so, how much extra will you have? If not, how much do you need?
11. A manufacturer offers you 6 payments of $800 per year for rights to your invention. Using a 7% discount rate with the first payment due immediately, how much cash would you accept right now in lieu of the annual payments?
12. Fran is starting a savings program. She will deposit $1,000 annually with the first payment made today. If she earns 10%, how long will it take to accumulate $7,000? Don’t forget to change your calculator to beginning mode.

Answer 1

a. Cecila on her 21st birthday has 25000 * (100%+6%)^21 = $84,989

b. Wade - If depositing at the start of the months - $7,912. If depositing at end of months - $8,018

Monthly requirement	(7,992)	=PMT(0.33%,24,,200000,1)
Interest per month	0.33%
Time in months	24
Amount required	200,000

c. Julie and Miguel require to invest $8,219 today to have $10,000 in 5 years

Amount required	10,000
Interest	4.00%
Period in years	5
Amount to be invested	8,219	=10000/(1+4%)^5

d. Bonus : Amount at the end of 3rd year = $37,091 (assuming that bonus will be received at year ends and amount is required at the end of 3rd year)

Yearly amount	12,000
years	3
Annual interest rate	3%
Amount at end of 3 years	37,091	=12000+12000*(1+D16)+12000*(1+D16)^2

e. Santiago: Amount to be invested at start of each month till 1.5 years =$189

Monthly requirement	(189)	=PMT(0.33%,24,,200000,0)
Interest per month	0.33%
Time in months	18
Amount required	3,500

f. Margaret : approximately 5.4 years (63.87 months)

Amount at period 0	6,500
Amount at end	12,600
Interest per month	1.04%
Months	63.87

g. Brian : Interest rate = 11.57% approximately

Value at start of year 1	1800
Value at end of year 3	2500
Period in years	3
Interest rate	11.57%	=(2500/1800)^(1/3)-1

h. Carol : Monthly payment of approx. $1,461

Total loan (400,000 * 70%)	280,000
Period in months	360
Interest rate monthly	0.3958%
Monthly payments	($1,460.61)	=PMT(0.3958%,360,280000,,)

Interest paid

(245,821)

i. Yearly investment of $150 at year end @ approximately 14.4% will accumulate $1,000 over 5 years

j. Car purchase

Amount today	15,000
Interest rate	8%
Years	3
Amount at end of 3 years with interest	18,896	=15,000*(1+8%)^3
Amount required at end of 3 years	23,000
Additional mount required	4,104

k. Manufacturer : Right now you should accept $4,080 in lieu of the annual payments

Interest rate	7%
Period	amounts to be received	Present value
right now	800	800	=800/(1+7%)^0
in 1 year from now	800	748	=800/(1+7%)^1
in 2 years from now	800	699	=800/(1+7%)^2
in 3 years from now	800	653	=800/(1+7%)^3
in 4 years from now	800	610	=800/(1+7%)^4
in 5 years from now	800	570	=800/(1+7%)^5
	Total	4,080

l. It will take slightly more than 5 years to accumulate $7,000 by investing $1,000 annually.