FNCE 2P91 Lecture Notes - Lecture 5: Investment, Interest

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ochreantelope751

17 Nov 2017

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Ch. 5 and 6 future values and compounding. Future value: the amount of investment is worth after one or more periods. Compounding: the process of accumulating interest in an investment over time to earn more interest. Compound interest: interest earned on both initial principal and the interest reinvested from prior periods. Interest on interest: interest earned on the reinvestment of previous interest payments. Simple interest: interest earned only on the original principal amount invested. Present value: the current value of future cash flows discounted at the appropriate discount rate. Discount: to calculate the present value of some future amount.

Related Questions

using excel, determine the future value of an amount deposited today, given an interest rate and the number of time periods. Be sure to use compound interest (interest rate applies to both principal and interest previously earned) versus simple interest (interest rate applies to only the principal).Suppose you currently have $10,000 and plan to purchase a 5-year certificate of deposit (CD) at your local bank that pays 4% interest, compounded annually. How much will you have when the CD matures? How would your answer change if the interest rate were 5%, or 6%, or 20%? Given the interest rate of 4%, how would your answer change if the CD term were 2-years or 3-years, or 10-years?

Problem 1: $3,000 is invested at 7.2% interest. Find the total amount (A) at the end of 5 years if:
a.) Simple interest is earned. (see the "Simple Interest Example" tab)
b.) Interest is compounded annually (see the "Compound Interest Illustration" tab)
c.) Interest is compounded quarterly (see the "Other Compounding Periods" tab)
d.) Interest is compounded monthly (see the "Other Compounding Periods" tab)
Problem 2: A department store charges 12% interest on the unpaid balance of customer charge accounts.
A customer owes $135, and the bill goes unpaid for 4 months. How much will the customer have to
repay after 4 months? Interest is compounded monthly (note that the 12% is an annual rate). (see the "Other Compounding Periods" tab)
Problem 3: A typical family of four spends approximately $600 per month for food. Food costs are
predicted to rise by 4.8% per year for the next 5 years. In five years, how much should
the family budget per month for food? Treat this as compound annual growth. (see the "Compound Interest Illustration" tab)
(assume annual compounding)
Problem 4a: A couple plans to begin saving money for a down payment toward the purchase of a home.
They plan to purchase a home 4 years from now. Right now, home prices are predicted
to rise by 5% per year for the next 5 years. If this prediction is accurate, how much
can this couple expect to pay in 4 years for a home that is currently valued at $210,000?
(what will be the total sales price in 4 years of a home worth $210,000 today?) (see the "Compound Interest Illustration" tab)
Problem 4b: The couple wants to have a 20% down payment on the purchase price in 4 years. Suppose they
have found a mutual fund that earns an average of 8% per year. How much should they invest in the
mutual fund today in order to have enough for a down payment in 4 years?
Assume annual compounding.
(Find the down payment first - that will be their "A" or future value of what they will invest)
(see the "Other Problem Types" tab - we are trying to find the principal or present value to be invested to grow to the down payment amount)
Problem 5: An electric company predicts that the cost of electricity will rise at the rate of 2% per
year for the next ten years. If the average monthly electricity for consumers in this area
is $225, predict the monthly amount that consumers can expect to pay 10 years from now.
(see the "Compound Interest Illustration" tab)

sangriabeetle691

Assume that you have $1,000 to invest, so insert 1000 as your Present Value in the following table. Assume that you want to invest your money for 5 years (insert 5 for Number of Periods). Assume an annual interest rate of 3.00% (insert 3 for Interest Rate per Period). The table will determine the Future Value of your investment. If you input the numbers correctly, your Future Value is computed to be $1.159, which is what your investment will be worth in 5 years. Now revise the input to reflect your actual savings and the prevailing interest rate so that you can see how your savings will grow in 5 years. Even if you have no savings now, you can at least see how the interest rate affects the future value of savings by revising your input in the Interest Rate per Period and then observing the change in the Future Value. Future Value of a Present Amount Present Value $1,500 Number of Periods 5 Interest Rate per Period 3.0% FV = PV*(1+R)^N Future Value $1,739 2. Assume that you have $1,000 to invest at the end of each of the next 5 years, so insert 1000 as your Payment per Period in the following table. Assume that you want to invest your money for 5 years (insert 5 for Number of Periods). Assume an annual interest rate of 3.00% (insert 3 for Interest Rate per Period). The following table will determine the Future Value of your investment. If you input the numbers correctly, your Future Value is computed to be $5,309, which is what your investments will be worth in 5 years. Now revise the input to reflect your actual expected savings per year over the next 5 years, and existing interest rate quotations so that you can estimate how your savings will grow in 5 years. You can now revise the table to fit your own desired level of saving. Future Value of an Annuity Payment per Period $1,500 Number of Periods 5 Interest Rate per Period 3.0% FV = FV(R, N, PMT, (PV), beginning=1, end=0) Future Value $7,964 3. Assume that you want to deposit savings that will be worth $10,000 in 5 years, so insert 10000 as the Future Amount and 5 as the Number of Periods in the following table. Assume an annual interest rate of 3.00% (insert 3 for Interest Rate per Period). The following table will determine the Present Value, which represents the amount of savings you need today that would accumulate to be worth $10,000 in 5 years. If you input the numbers correctly, the Present Value is estimated in the table to be $8,606. Now revise the input to reflect your own desired savings amount in 5 years so that you can estimate how much you need now to achieve your savings goal in 5 years. Present Value of a Future Amount Future Amount $20,000 Number of Periods 5 Interest Rate per Period 3.0% PV = FV / (1+R)^N Present Value $17,252 4. Assume that you want to deposit savings at the end of each of the next 5 years so that you will have $10,000 in 5 years. So insert 10000 as the Future Amount and 5 for Number of Periods. Assume an annual interest rate of 3.00% (insert 3 for Interest Rate per Period). The following table will determine the Annual Payment, which represents the annual payments that will accumulate to your future desired investment. If you input the numbers correctly, your Annual Payment is computed to be $1,884. Now revise the input to reflect your own desired savings amount in 5 years so that you can estimate how much you need to save per year to achieve your savings goal in 5 years. Compute Payment Needed to Achieve Future Amount Future Amount $20,000.00 Number of Periods 5.00 Interest Rate per Period 3.00% PMT = FV / [FV(R, N, -1)] Annual Payment $3,767

Decisions 1. Using the above formulas and understanding of the impact of interest rates and time on your savings, report on how much you must save per year and the return you must earn to meet your savings goal for graduation, and your savings goal in your first three years of post-graduation life.

I need a report on how much to save per year and the return to earn to meet savings goal for graduation, and savings goal in the first three years of post graduation. Can you please use the numbers above that are already calculated in the formula. I have had an answer on this below. I don't understand why the periods don't stay the same for 5 years. The annuity is 7964 I took that divided b y 60 = 132.7 per month and multiplied it by 12 for a year and got 1592.4. Is that the savings for the answer to saving for a year. IF not I need help figuring out the calculation for the return to meet after gradutaion and the next three years post graduation.

Goal 1	Savings Goal for graduation, FV	$ 20,000

	Time till graduation (Number of periods)	5

	Present value of savings	$ -

	Expected interest rates	3%

	Savings needed per year, PMT	$3,767.09	=PMT(3%,5,0,20000,)

Goal 2	Savings Goal for 1st year of post graduation, FV	$ 15,000

	Time till post graduation year 1 (Number of periods)	6

	Present value of savings	$ -

	Expected interest rates	3%

	Savings needed per year, PMT	$2,318.96	=PMT(3%,6,0,15000,)

Goal 3	Savings Goal for 2nd year of post graduation, FV	$ 15,300

	Time till post graduation year 1 (Number of periods)	7

	Present value of savings	$ -

	Expected interest rates	3%

	Savings needed per year, PMT	$1,996.75	=PMT(3%,7,0,15300,)

Goal 4	Savings Goal for 3rd year of post graduation, FV	$ 15,606

	Time till post graduation year 1 (Number of periods)	8

	Present value of savings	$ -

	Expected interest rates	3%

	Savings needed per year, PMT	$1,754.99	=PMT(3%,8,0,15606,)

FNCE 2P91 Lecture Notes - Lecture 5: Investment, Interest

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