Question

1. An entrepreneur borrows $275,000 today. The interest rate is 8%. Finally, the loan needs to be paid off in equal annual installments over the next 12 years, starting one year from today. How much will the entrepreneur have to pay each year?

a. 22917

b. 22000

c. 36491

d. 44917

2. Suppose that you just turned 30 and that you would like $6 million at age 70 to fund your retirement. You would like to save each year an amount that grows by 5% each year (that is, if you save $1 this year, you will save $1.05 next year). Assume that the discount rate is 9%. How much should you start saving at the end of this year? (Hint: first calculate the present value of the $6 million, then use the growing annuity formula to calculate the amount you must save at the end of this year).

a. 10072

b. 4776

c. 150000

d. 9848

Answer 1

1)	Present value of an annuity = C*[(1-(1/(1+r)^t))/r]
	where C is the annuity payment
	r is the interest rate that is 8%.
	t is the time period in years that is 12.
	The present value of the annuity is 275000.
	C*[(1-(1/((1.08)^12))/.08] = 275000
	C*[(1-(1/(2.5182))/.08] = 275000
	C*[(1-.3971)/.08] = 275000
	C*[(.6029)/.08] = 275000
	C*[7.5361] = 275000
	C = 275000/7.5361
	C = 36491.13
	The entreprenuer will have to pay $36491 every year.
	c) $36491.
2)	Find the present value of 6 million that you want to have in 40 years.
	That will be the present value of the growing annuity.
	Present Value = Future value/ ((1+r)^t)
	where r is the interest rate that is 9% and t is the time period in years that is 40.
	Future value	6000000
	Present Value	6000000/((1.09)^40)
	Present Value	191025.5
	The present value of the growing annuity is $191025.5.
	The present value of a growing annuity = C*[1-((1+g/1+r)^t)/(r-g)]
	g	0.05
	r	0.09
	t	40
	191025.5 = C*[1-((1.05/1.09)^40)/(.09-.05)]
	191025.5 = C*[1-((.963303)^40)/(.04)]
	191025.5 = C*[1-(.224136)/(.04)]
	191025.5 = C*[(.775864)/(.04)]
	191025.5 = C*[19.39659]
	C = 191025.5/19.39659
	C = 9848.404
	The amount you should save at the end of this year
	d) $9848.