Question

a )A lender offers you a mortgage with an APR of 4.20% with monthly compounding. What is the effective rate of interest charged by the lender?

b) An investor is considering an opportunity that pays the following cash flows:

Year	1	2	3
Cash Flow	$110.00	$132.00	$151.00

The investor thinks interest rates will rise over the next few years, so he wants to use different rates based on the year. For the first year, he will use a discount rate of 3.69%. For the second year, he will use 5.91%, and for the third year, he will use 7.44%. Find the value of this investment today.

c) A real estate investment has the following expected cash flows:

	Year	Cash Flows
	1	$10,600.00
	2	$26,800.00
	3	$35,100.00
	4	$42,500.00

The discount rate is 6.00 percent. What is the investment's future value at the end of the fourth year?

Answer 1

a.

APR with monthly compounding = 4.2%

APR with annual compounding = (1 + 0.042/12)¹² -1

APR with annual compounding = 4.28%

b.

Taking cash flows as end of the year cash flows

Value of Investment today = 110/(1.0369) + 132/(1.0591)² + 151/(1.0744)³

Value of Investment today = 106.085 + 108.47 + 121.75

Value of Investment today = $336.31

c.

Future Value at the end of 4th year = 10600(1.06)³ +26800(1.06)²+35100(1.06)¹ + 42500

FV of Investment = 12624.77 + 30112.48 + 37206 + 42500

FV of Investment = 122,443.25