Time Value of MoneyThe Basics Compare some of the different

Time Value of Money-The Basics Compare some of the different financial calculators that are available on the et Look at Kiplinger Online calculators (www.kiplinger.comools/index ntml) which include saving and investing, mutual funds, bonds, stocks, home, auto credit c w ards, and budgeting online calculators. Also go to www.dinkytown.net www.bankrate ate.comcalculators.aspx, and www.interest.com and click on the \"Calcu lators\" links, Which financial cakculators do you find to be the most useful? Why Related to Chapter Introduction: Payday Loans) The introduction to this chapter ex amined payday loans. Recently, Congress passed legislation limiting the interest rate charged to active military to 36 percent. Go to the Predatory Lending Association wcbsate at www.predatorylendingassociation.com and find the military base closest o you and identify the payday lenders that surround that base. Also, identify any payday lenders near you S. (Related to Chapter Introduction: Payday Loans) In the introduction to this chapter, payday loans were examined. Go to the Responsible Lending Organization website at www.responsiblelending.org/payday-lending. How does the \"debe trap\" (www with payday loans work? ing orgipayday-lendingtools-resources/debtrap.html) associated Study Problems MyFinanceLab Compound Interest Go to www.myfinancelab.com to complete these exerdibes onine and get instant foodback Related to Checkpoint 2) (Future value) To what amount will the folliowing invest- ments accumulate? a. $5,000 invested for 10 years at 10 percent compounded annually b. $8,000 invested for 7 years at 8 percent compounded annually c. $773 invested for 12 years at 12 percent compounded d. $21,000 invested for 5 years an 5 percent compounded annually 2. (Related to Checkpoint 2) (Future value) Leslie Mosallam, who recently sold her Porsche, placed $10,000 in a savings account paying annual compound interest of 6 percent. a. Calculate the amount of money that will accumulate if Leslie leaves the money in the bank for 1, 5, and 15 years b. Suppose Leslie moves her money into an account that pays 8 percent or one that pays 10 percent. Rework part (a) using 8 percent and 10 percent. c. What conclusions can you draw about the relationship between interest rates, time, and futare sums from the calculations you just did? (Related to The Business of Lifec Saving for Your First House) (Future value) You are hoping to buy a house in the future and rocently received an inheritance of $20,000, You intend to use your inhentance as a down payment on your house. a. If you put your inheritance in an account that eams a 7 percent interest rate compounded anaually, how ma ny years will ia be before your imheritmce grows to h. If you let your money grow for 10.25 years at 7 percent, how much will you have? c. How long will it take your money to grow to $30,000 if you 3 percent compounded annually? How long will it take your money to grow to $30,000 if you move it into an account that pays 11 percent does all of this tell you about the relationship ansong interest rates, time, and future sums? to Checkpoint 2) (Future value) Bob Terwilliger received $12,345 for 4. (Related s financial consultant to the mayor\'s office of his hometown of savs that his consulting work was his civic duty and that he should Springfield. Bob not receive any compensation. So, he has in vested his paycheck into an account ent annual interest and left the account in his will to the city of ing 3.98 Springfield on the condition that the city could not collect any money from 167

Solution

1 Given: Principal, Rate of Interest and number of years.

         To Calculate : Future Value

Future Value = Principal* ( 1+rate in decimals)^number of years

1(a) Future Value ( FV) = 5000* ( 1+.1)^10

                                      = 5000*(1.1)^10

                                     =5000*2.5937425

                        Answer:             =$12968.712

1 (b) Principal= $8000 Nos of years = 7 Interest = 8%

Using the same formula as above in 1(a)

FV= 8000*(1.08)^7= 8000*1.7138243

Answer: $13710.594

1(c) P= $ 775 Nos of years =12 Interest =12%

       FV= 775*(1.12)^12= 775*3.895976

Answer: $ 3019.381

1(d) P= $21000 Nos of years = 5 Interest = 5%

FV= 21000*(1.05)^5

= 21000*1.2762816

Answer: $26801.91

3(a) Given: Inheritance amount = $20,000

If invested at 7% per nnum compounded annually, we need to calculate the number of years it will take to become $ 30,000.

Again using the formual stated in 1 above: Future Value = Principal* ( 1+rate in decimals)^number of years

=> 30,000= 20000(1.07)^x

=> 30000/20000= 1.07^x

=> 1.5= 1.07^x

We can find X by using log tables or excel or just multiplying 1.07by itself a number of times.

If we use the last method we find 1,07X1.07X1.07X1.071X1.07= 1.5

In other words it will take 5 years for $20,000 to become $30,000 when invested at 7% compounded annually.

3 (b) If we invested the $20000 at 7% compounded annually for 10.25 years

we get FV= 20000*(1.07)^10.25

                 = 20000*2.000708

                  = Answer: $40,014.16

3(c) In this case we need to find the number of years it will take for the $20,000 to grow to $ 30,000 if invested at 3% and if invested at 11%.

If invested at 3% : 30000= 20000*(1.03)^x or

                              30000/20000= 1.03^x

                              1.5= 1.03^x

This is roughly 15 years.

If invested at 11%

                    it will be 1.5= 1.11^x

This is roughly 4 years.

Ans 3(d) All this tells us that when we invest at a higher rate and for a longer period of time the future value gets increased many times. This is the compounding effect of money. Higher the interest rate or higher the period of investment or both will result in higher returns.

The trick here is in calculating the exponential value. You can use Log tables ( learnt from maths) or a calculator or excel or intutively as well by manually multiplying that many number of times to get an answer.

5. Compound Interest with non-annual periods:

When we have to calculate compound Interest with non-annual periods we need to divide the interest rate by the number of periods and multiply the years by the number of periods.

For eg. if we are investing at 10% compounded two times a year for 5 years then the

Rate of interest becomes 10/2= 5% and the number of years becomes 5*2 = 10 years

After this we apply the same formula Amount= Principal* ( 1+ rate of Int) ^ nos of years.

The below table provides the answers in each of the given case:

Hope this helps.

11) Given that we are investing $10,000 at 11% interest.

The formula for Simple interest = Principal * Rate of Interest* nos. of years

Principal - $10000 Rate if int =11% or 0.11 Nos of years = 3

Simple Interest= 10000* 0.11 * 3

= 3300.

Compound interest = Principal *( 1+ Interest)^nos of years - Principal

=10000 *(1.11)^3= 10000*1.367631-10000

= 13676.31- 10000

=3676.31

Therefore the total interest earned is $. 3676.31 out of which $3300 is on account of Simple interest and the extra

$ 376.31 is on account of the compounding effect.

I have answered questions 1 ( all four parts), Q 3, Q5 and Q 11.

Account Holder	Amount Deposited	Annual Interest Rate		Compounding period	Years	Amount
Theodore Logan III	1000	0.10		1	10	2593.7425
Vermell Coles	95000	0.12		0.12	1	103239.81
Tina Elliot	8000	0.12		6	2	10145.934
Wayne Robinson	120000	0.08		4	2	140599.13
Eunice Chung	30000	0.1		2	4	44323.663
Kelly Cravens	15000	0.12		3	3	21349.677