ECON 2560 Lecture Notes - Real Interest Rate

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purplegiraffe992

9 Jul 2014

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Note: unless otherwise stated, assume that cash flows occur at the end of each year. To find the interest rate, we rearrange the equation. Fv = pv (1 + r)n to conclude that r = ()1/n - 1. To use a financial calculator for (a) enter pv= (-)400, fv = 684, pmt = 0, n = 11 and compute the interest rate. The present value of your payments to the bank equals: annuity factor(8%, 10 years) = . 01. The present value of your receipts is the value of a perpetuity deferred for 10 years: This is a bad deal if you can earn 8% on your other investments. By the time you retire you will need. ,000 future value annuity factor(5%, 20 periods) = ,488. 41. The future value of the payments into your savings fund must accumulate to. We choose the payment so that pmt future value of an annuity =

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1. Cash Flow Diagrams and Compounded Interest: John decides to take out a loan for $10,000 for school at an annual interest rate of 10%. He agrees to make four equal payments, but will defer these payments for four years while in school. Starting at the end of the 5^th year, he makes four equal annual payments (years 5, 6, 7 and 8). At the end of the 8^th year, the loan is paid off.

(a) Create a table that depicts the cash flow diagram for this problem. It should cover years 0 to 8, and should show the balance, interest charges, each payment, how much of that payment went towards interest and how much towards the principal. The balance should be zero at the end of the 8^th year. Use trial and error to find the required payment.

(b) Compute the annual payment using one of the built-in Excel functions discussed in class. Show that this gives the same answer as (a).

(d) Suppose interest is compounded twice per year instead of annually, but he still makes four annual payments starting at the end of the 5^th year. What is the new annual payment?

2. Kate will purchase a house for $500,000 with a 10% down payment and $10,000 in closing costs. The closing costs are included in the loan. A 10-year loan is arranged at 5% interest compounded monthly.

(a) What is the monthly payment?

(b) By choosing to include the closing costs in the loan, how much money was paid in interest on the closing costs over the life of the loan.

(c) What is the effective interest rate for this loan? (Hint: you must take into account the monthly compounding AND the closing costs.)

(d) Suppose closing costs were paid at closing. How does this change the overall cost of the loan? How does this change the effective interest rate?

(NOTE: EVERYTHING SHOULD BE DONE IN EXCEL. OTHERWISE NO POINTS. INCLUDE THE FUNCTION USED AS WELL)

greensardine434

You have $35,259.87 in a brokerage account, and you plan to deposit an additional $2,500 at the end of every future year until your account totals $350,000. You expect to earn 11.7% annually on the account. How many years will it take to reach your goal? Round your answer to the nearest whole number.

2)What is the future value of a 10%, 5-year ordinary annuity that pays $550 each year? Round your answer to the nearest cent.

If this were an annuity due, what would its future value be? Round your answer to the nearest cent.

3)An investment will pay $100 at the end of each of the next 3 years, $300 at the end of Year 4, $500 at the end of Year 5, and $700 at the end of Year 6. If other investments of equal risk earn 9% annually, what is its present value? Round your answer to the nearest cent.

What is its future value? Round your answer to the nearest cent.

4)You want to buy a car, and a local bank will lend you $10,000. The loan would be fully amortized over 6 years (72 months), and the nominal interest rate would be 10%, with interest paid monthly. What is the monthly loan payment? Round your answer to the nearest cent.

What is the loan's EFF%? Round your answer to two decimal places.

Present and Future Values of Single Cash Flows for Different Periods

Find the following values, using the equations, and then work the problems using a financial calculator to check your answers. Disregard rounding differences. (Hint: If you are using a financial calculator, you can enter the known values and then press the appropriate key to find the unknown variable. Then, without clearing the TVM register, you can "override" the variable that changes by simply entering a new value for it and then pressing the key for the unknown variable to obtain the second answer. This procedure can be used in parts b and d, and in many other situations, to see how changes in input variables affect the output variable.)

An initial $800 compounded for 1 year at 5.6%. Round your answers to the nearest cent.

$
An initial $800 compounded for 2 years at 5.6%. Round your answers to the nearest cent.

$
The present value of $800 due in 1 year at a discount rate of 5.6%. Round your answers to the nearest cent.

$
The present value of $800 due in 2 years at a discount rate of 5.6%. Round your answers to the nearest cent.

coralwolf381

Monetary Policy and Inflation: Use our standard Keynesian macroeconomic model:

â¢ Y = E = C + I + NX + G â GDP equals the sum of consumption, investment, net exports, and government purchases
â¢ C = c0 + cy x Y â consumption equals the consumer-confidence term plus the mpc times GDP or income
â¢ I = I0 - Ir x r â business investment spending equals the business animal-spirits term minus the interest sensitivity of investment times the long-run real risky interest rate
â¢ Î¼ = 1/(1 - cy) â the multiplier is the inverse of one minus the mic
â¢ Y = Î¼(c0 + I0 + NX) - (Î¼ Ir) x r + Î¼G â our summing-up equation, telling us how the level of annual GDP depends on the multiplier Î¼, on the private spending flows c0 + I0 + NX, on the
interest-sensitivity parameter Ir, on the interest rate r, and on government purchases G

For this problem, assume a value of the Keynesian multiplier of Î¼ = 2, and with Ir, the sensitivity of investment spending I to the interest rate r, such that Ir = $0.15T. And letâs use the Greek letter Îâcapital deltaâas a shorthand symbol for changes from the previous equilibrium situation.

The Federal Reserve controls the short-term safe interest rate on government securitiesâit can nail that value to whatever it wants by buying and selling bonds for cash. We call this interest rate i. But the interest rate that matters for determining investment spending is the long-term real risky interest rate at which banks lend to companies. We call this interest rate r.

a) Suppose that the interest rate r that matters for investment spending falls by 1.5%-pts:
Îr = -1.5
By how much would you expect investment spending to fall given the parameter values of our model? How large is ÎI?

b) Continue your analysis from (a): given the parameter values of our model and the boosting of investment spending you calculated in (a), by how much would you expect GDP Y to grow?

c) Annual real GDP in the mid-2000s was about $15T. How large is this boost to GDP ÎY you calculated in (b) as a percentage of the then-level of real GDP?

d) On average, a 1% extra boost to GDP is associated with a 1.5% extra decrease in the unemployment rate. By how much extra would you expect the unemployment rate to fall as a
result of the boost to GDP you calculated in (b) and (c)?

e) Suppose that with the interest rate decline the unemployment rate falls from 6% to 4.5%. What would the unemployment rate have been without this interest-rate decline?

f) Suppose that real GDP had been lower for each of three years by the amount you calculated in (b). How much poorer would Americans have been in terms of reduced income over those three years had the interest rate r not fallen?

g) In an America with about 135 million workers, how much is this lost income per worker?

ochredonkey719

ECON 2560 Lecture Notes - Real Interest Rate

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