Question

REMEMBER!!l: you must always adjust the rate and term in the formula asI have done above (note the 6%12, 5 x 12). If you do not use this format when solving this problem, I will not read your homework answers. This format is used for the tests too. (You may have to use this format more than once in a problem if it is a multipart problem.) REMEMBER: You must ALWAYS ALWAYS ALWAYS adjust the rate and term to match the time period of the payments. You NEVER EVER add up values from ditferent years (yes this is a repeat) However, you CAN add up values occurring in the same time period. No Spacing Normal Heading 1 5. Refer to problem #4. What would your answer be if the rate were 18%? 6. Based on your answers from #5 and # 4 , complete this sentence: The higher the interest rate, the the present value. WHY is this true?? Write your answer to this question BELOW your answer to this question. Your answer is important to remember-It is an important characteristic of rates in TVM and comes up later in later chapters. 7. Marianna wants to save $300 every 6 months (semi-annually) for the next 10 years. How much will she have if the interest rate is 8%? I 8. Your great Aunt loves you a lot and wants to give you some money. The only thing is that she loves finance and so, naturally, always makes it a bit of a challenge to get her money She promises to pay you the following cashflow: $1500 in 1 year, $2,600 in year 2 and $3,000 in year 3. You have to tell her how much she must set aside in an account to meet those cash payments. Assume a 10% rate. 9 Your Aunt's best friend want to also give you some money but has another TVM problem for you: She will give you $200 every 3 months for 10 years AND in addition to the last $200 payment she will also give $10,000 to you (in year 10). Her question is how much does she have to set aside today in order to meet this cash flow Assume a rate of 12% (Hint this has TWO TVM cash flows in it Solve each separately and, since your answer will be in the same time period, add the two values up for a final answer). ok Air 12% (Hint this has TWO TVM cash flows in it Solve each separately and, since your answer will be in the same time period, add the two values up for a final answer). 10. You are going to borrow $100,000 for a home loan for T0 years. If the payments are $1,801.85/month, what is the interest rate on this loan tremember all rates are always quoted as annual equivalents)? Hint: set up timeline and determine which type of TVM problem it resembles and use that to solve with the same formula you used for all of the problems above. The only thing different here is the unknown is now the factor.

Answer 1

Question 6.

The higher the interest rate, the lower the present value.

If the interest rate is higher then we have to set aside less amount in present to achieve the specific amount in future. Hence higher interest rate results in less amount required in present to save.

Question 7.

Future value = Present value * ( 1 + r)ⁿ

r = 8% Semi annually = 8%/2 = 4%

n = 10 Years * 2 = 20 Years

Future value = $300 ( 1 + 0.04 )²⁰

= $300 * 2.19

= $ 657

She will have $657 after 10 years.

Question 8.

Present value = Future value * Present value factor

Present value factor =

Year 1 = 1 / ( 1 + r )¹

Year 2 = 1 / ( 1 + r )²

Year 3 = 1 / ( 1 + r )³

Interest rate = 10%

Year	Cash flow	PVF	Present Value
1	1500	0.909	1363.5
2	2600	0.826	2147.6
3	3000	0.751	2253.0
Total			5764.1

She must set aside $5764.10 to meet the cash payment.

Question 9.

Cash flow = $200

Last payment = $10000

Rate of interest = 12%

Payment made = In every 3 months.

Quarterly interest rate = 12% / 4 = 3%

No of period = 10 years * 4 = 40 times

Present value for uniform cash flow = Future value * Present value annuity factor

Present value annuity factor = 1 / ( 1 +r)¹ + 1 / ( 1 + r)² + 1 ( 1 +r)³+.....................................1 / ( 1 + r )⁴⁰

Present value for last payment = Future value * ( 1 + r )¹⁰

Here R = 12%

N = 10 Years Since there is only one time payment.

Present value for uniform cash flow = ($200 * 23.11)

= $4622.95

Present value for last payment = $10000 * ( 1 .12 )¹⁰

= $10000 * 0.322

= $3220

Total amount required to set aside = ( $4622.95 + $3220 ) = $7842.95