Question

please answer all in full

1. On your 1st birthday, you received a $10 savings account earning 6% annually. How much will you have in the account on your 30th birthday if you don't withdraw any money before then?

2. Your partner just promised to you that he/she will give you a graduation gift by paying half of of a new car when you receive an MBA degree in 2 years. Suppose that you also have $9,000 to invest today for your car and can earn 12% on the investment. If your partner match the amount of money you have in two years, what is the maximum you can spend on the new car?

3. Homer (the father) promises Bart (the son) that he will give him $8,000 upon his graduation from college at Springfield U. How much must Homer invest today to make good on his promise, if Bart is expected to graduate in 13 years and Homer can earn 6% on his money?

4. You are a rising superstar, and your boss offers you a contract-ending bonus of $10 million after 3 years of service. However, you would like to receive the money right now. If the prevailing interest rate is 5% per year, how much should you ask for now?

5. In 1889, Vincent Van Gogh's painting "Sunflowers" was sold for $125. One hundred years later it sold for $36 million. Had the painting been purchased by your great-grandfather and passed on to you, what annual return on investment would your family have earned on the painting?

6. Ten years ago, an account was opened with an investment of $2,000. The ending balance in the account now is $3,500. If interest was compounded annually, what rate was earned on the account per year?

7. Your grandma has put $25,000 into a trust account on your behalf, but stipulated that you cannot withdraw the money until the balance has doubled. How long will you have to leave the money in the account if it earns 6% a year.

8. A long-lost relative has just given you an inheritance of $100,000. If you invest the money and it earns at 7% annually, how long will it take for you to become a millionaire?

9. Many economists view a 3% annual inflation rate as "acceptable". Assuming a 3% annual increase in the price of automobiles, how much will a new Tesla cost you 8 years from now if today's price is $40,000?

10. You are looking at two savings accounts. One pays 5.25% (APR), with daily compounding. The other pays 5.3% (APR) with semiannual compounding. Which one would you choose? Why?

11. Suppose that you have decided to set aside $300 per month and invest in a retirement account. Assuming the investment account earns 1% a month (12% APR), how much money would you have in your retirement account by the time you retire at 65? Assume your current age is (i) 30 years; (ii) 35 years; (iii) 40 years; (iv) 45 years; and (v) 50 years.

12. Now let's work backwards. Assume that you will all live until 100 (a good news!), but will have to retire by 65 (a bad news^^). You estimate that you will need to draw at least $3,000 per month of living expenses out of your retirement account after you retire (assume no inflation). Suppose that your retirement account will keep earning 6% APR after you retire. If you want to ensure that your retirement account will not run out of money before the age of 100, how much should you have in your retirement account when you retire at 65?

13. Given your answer to Question 12 and your current age, how much should you save and put into the retirement account per month to achieve the goal at 65? Assume that you can earn 6% APR with monthly compounding on your investments.

14. You took a mortgage loan of $300,000 to buy a condo apartment, and agreed to pay the loan over 30 years on a monthly basis. Suppose your bank says they are charging 5% APR but the interest rate is charged on a daily basis on the remaining principal. How much do you have to pay per month (equal amount) to pay off all of your debt in 30 years?

15. Suppose your goal is to retire in 20 years from now with $10 million. How much should you invest per month if your invested funds can earn 12% APR (with monthly compounding) in order to achieve the goal?

Answer 1

	1	FV=PV*((1+i)^N)
		PV=Present Value =$10
		i= interest rate=6%=0.06
		N=Number of Years=(30-1)=29
		Fv=Future Value =10*(1.06^29)=	$54.18
		Amount in account on 30th birthday	$54.18
	2	PV=Present Value =$9000
		i= interest rate=12%=0.12
		N=Number of Years=2
		Fv=Future Value =9000*(1.12^2)=	$11,289.60
		Maximum amount can be spent =2*11289.60	$22,579.20
	3	FV=Future Value =$8000
		i= interest rate=6%=0.06
		N=Number of Years=13
		Pv=Present Value =8000/(1.06^13)=	$3,750.71
		Amount to be invested today	$3,750.71
	4	FV=Future Value =$10,000,000
		i= interest rate=5%=0.05
		N=Number of Years=3
		Pv=Present Value =10000000/(1.05^3)=	$8,638,376
		Amount to be received right now	$8,638,376