Time Value of Money
Compounding – The process of determining the value of a cash flow or series of cash flows at some point in the future when compound interest is applied.
Discounting – The process of finding the present value of a cash flow or series of cash flows; the reverse of compounding.
Time Line – A graphical representation used to show the timing of cash flows. If not otherwise stated, assume that the cash flow(s) occur at the end of the period indicated.
Terminology
PV0 = present value (normally at t = 0)
FVn = future value at the end of n periods
i = interest rate, discount rate, required rate of return, etc.
n = number of periods interest is earned
m = the
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Compute the future value of $1,580 if the appropriate rate is 5.4% and you invest the money for four years? What is the future value if you invest for eight years?
2. Your uncle plans to buy a piano and can afford to set aside $1,930 toward the purchase today. If the annual interest rate is 14.8%, how much can he spend in four years on the purchase? If the interest rate is 7.4%, how much can he spend?
3. You plan to buy a lawn tractor and can afford to set aside $1,470 toward the purchase today. If the annual interest rate is 5.5% compounded every quarter, how much can you spend in two and half years on the purchase? If you invest for five years, how much can you spend?
4. Joe plans to buy an antique lamp set and can afford to set aside $980 toward the purchase today. If the annual interest rate is 11.7% compounded every week, how much can Joe spend in
academic year interest rate of 3.76 percent would pay a 5,032 dollars interest over 10 years,
Poor Dog, Inc. borrowed $135,000 from the bank today. They must repay this money over the next six years by making monthly payments of $2,215.10. What is the interest rate on the loan? Express your answer with annual compounding.
1. Beverly Frost bought a home for $190,000 with a down payment of $19,000 at 7% for 25 years. Since then the rate has risen to 9%. How much more would her monthly payment be if she bought the house at 9%?
7. Trevor's Tires is offering a set of 4 premium tires on sale for $550. The credit terms are 24 months at $20 per month. What is the interest rate on this offer?
b. If you inherited $100,000 today and invested all of it in a security that paid an 8% rate of return, how much would you have in 15 years?
What annual interest rate is needed to produce $200,000 after five years if only $100,000 is invested?
1. Community Hospital has annual net patient revenues of $150 million. At the present time, payments received by the hospital are not deposited for six days on average. The hospital is exploring a lockbox arrangement that promises to cut the six days to one day. If these funds released by the lockbox arrangement can be invested at 8 percent, what will the annual savings be? Assume the bank fee will be $2,000 per month.
10. An investment of $1,000 today will grow to $1,100 in one year. What is the continuously compounded rate of return?
Therefore the annual interest rate is 8% and the effective annual rate compounded quarterly is 8.24%
8. If you want to purchase a home. You have $15,000 to put down. All you can afford is $1,500.00 per month and you do not want to finance for more than 15 years @ 6% interest, (your taxes will be $85.00 per month and insurance $200.00 a month), what is the amount you can pay for your home? (Show all your work)
At an interest rate of 15% per year (3.75% for three months, the amount to borrow equals
After the calculations you end up coming out with a rate of 14.87%. The third and final part of question three asks what rate you will need if the interest is compounded semiannually. All you have to do is double the amount of terms and you will come out with a lower number of 7.177%. Since the interest is compounded semiannually that means that you will need to times that number by two and you come out with your final number of 14.35%.
13. Compounding is the process of converting today's values, which are termed present value, to future value.
(Compound value solving for I) at what annual rate would the following have to be investe
3. John had $30,000 to invest. He invested part of this money in bonds paying 12% annual simple interest and the rest of the money in a savings account giving 4% annual interest. At the end of the year, he received $2,400 as extra income. How much money did John place in each investment?