Question

1.If the applicable discount rate is 12%, what is the present value of the following stream of cash flows? Round to the nearest cent. Cash Flow Year 1: $4,000 Cash Flow Year 2: $12,000 Cash Flow Year 3: $12,000 2.Someone says they’ll give you $19,000 in exactly 8 years. If the applicable discount rate is 10%, compounded annually, how much would you be willing to loan them today in exchange? Round to the nearest cent. 3.You’d like to buy a small ranch when you retire in 39 years. You estimate that in 39 years you’ll need $8 million to do so. If you can earn 1.1% per month, how much will you need to invest each month (for 39 years), starting next month, in order to reach your goal? Round to the nearest cent 4.You purchase a house, and must borrow money from the bank to do so (a mortgage). You borrow $343,000 to be paid back over 30 years in monthly installments (starting in month 1). If the interest rate is 4% per year, what is your monthly mortgage payment? Round to the nearest cent

Answer 1

Answer 1:

Present value = Cash Flow Year 1/ (1 + discount rate) + Cash Flow Year 2 / (1 + discount rate) ² + Cash Flow Year 3 / (1 + discount rate) ³

Present value = 4000 / (1 + 12%) + 12000 / (1 + 12%) ² + 12000 / (1 + 12%) ³

= $21,679.12

Present value = $21,679.12

Answer 2:

PV = FV / (1 + Discount rate) ^{Number of years}

= 19000 / (1 + 10%) ⁸

= $8,863.64

You would be willing to loan them today in exchange = $8,863.64

Answer 3:

Time period = 39 years = 39 * 12 = 468 months

Amount required after 39 years = $8 million = $8,000,000

Monthly Interest = 1.1%

To get monthly investment required, we will use PMT function of excel:

PMT (rate, nper, pv, fv, type)

= PMT (1.1%, 468, 0, -8000000, 0)

=$529.11

Amount you need to invest each month =$529.11

Answer 4:

Loan amount = $343,000

Number of monthly installments = 30 * 12 = 360

Monthly interest rate = 4%/12

To get monthly payment required, we will use PMT function of excel:

PMT (rate, nper, pv, fv, type)

= PMT (4%/12, 360, -343000, 0, 0)

= $1637.53

Monthly payment required = $1,637.53