Session 5 Homework Time Value of Money - Answer the following questions: 1. Assu

Question

Session 5 Homework

   Time Value of Money - Answer the following questions:

1. Assume that 1 year from now; you will deposit $1,000 into a savings account that

     pays 8%.

a.     If the Bank compounds interest annually, how much will you have in your account 4 years from now?

b.     What would your balance 4 year from now be if the bank used quarterly compounding rather than annual compounding?

c.     Suppose you deposited the $1,000 in 4 payments of $250 each at Years 1, 2, 3, and 4. How much would you have in your account at Year 4, based on 8% annual compounding?

2.     Assume that 4 years from now you will need $1,000. Your bank compounds interest at an 8% annual rate.

a.     How much must you deposit 1 year from now to have a balance of $1,000 4 years from now?

b.     If you want to make equal payments at Years 1 through 4 to accumulate the $1,000, how much each of the 4 payments be?

c.     If your father were to offer either to make the payments calculated in part b or to give you a lump sum of $750 1 year from now, which would you choose?

d.     If you have only $750 1 year from now, what interest rate, compounded annually, would you have to earn to have the necessary $1,000 4 years from now?

e.     Suppose you can deposit only $186.29 each at Years 1 through 4, but you still need $1,000 at Year 4. What interest rate, with annual compounding, must you seek out to achieve your goal?

3.      Find the amount to which $500 will grow under each of the following conditions:

a.     12% compounded annually for 5 years

b.     12% compounded semiannually for 5 years

c.     12% compounded quarterly for 5 years

d.     12% compounded monthly for 5 years

4.     While Mary was a student at the University, she borrowed $12,000 in student loans at an annual interest rate of 9%. If Mary repays $1,500 per year, how long, to the nearest year, will it take her to repay the loan?

5.     You win a lottery that pays you $100 a year for ever and agrees to pay all of your ancestors $100 forever. What is the present value of your winnings?

Explanation / Answer

A1a)

4 years from now, the annually compounded value would be 1000*(1+8%)(4-1) = $ 1,259.712 or $ 1259.71

A1b)

4 years from now, the quarterly compounded value would be 1000*(1+(8/4)%)(4-1)*4 = $ 1,268.242 or $ 1268.24

A1c)

Compounded value at 4 years = 250*(1+8%)(4-1) +250*(1+8%)(4-2)+250*(1+8%)(4-3)+250*(1+8%)(4-4) = $ 1126.528 or $ 1126.53

A2a)

Let the value invested be X.

Hence, X(1+8%)(4-1)= 1000 => X = $ 793.83

A2b)

Let the instalment be X.

Hence X*(1+8%)(4-1) +X*(1+8%)(4-2)+X*(1+8%)(4-3)+X*(1+8%)(4-4) = 1000

Hence X = $ 221.92

A2c)

Value of $750 given after a year, accumulated 4 years from now = 750*1.08^3 = 944.784 < 1000.

Hence we should take the instalments and not the lumpsum amount.

A2d) Let interest rate be r.

Hence, 750*(1+r)^3 = 1000 => r = 10.06424%

A2e) Let interest rate be r.

Hence,  $186.29*(1+r)(4-1) +$186.29*(1+r)(4-2)+$186.29*(1+r)(4-3)+$186.29*(1+r)(4-4) = 1000

=> r = 20%

A3)

a) $500 * (1+12%)^5 = $ 881.17

b) $500 * (1+12%/2)^(5*2) = $ 895.4238 or $ 895.42

c) $500 * (1+12%/4)^(5*4) = $ 903.0556 or $ 903.06

d) $500 * (1+12%/12)^(5*12) = $908.3483 or $ 908.35

A4) NPV of all cash flows = 0 (discunted payback)

Hence, 15 years = answer

Rate of return r 9.00% Formula Case -> A Cash flow PV of Cash flow Year Cash flow PV of cash flow Cumultive PV of cash flows Discounted pay back period N (years when cumulative cash flow =0) A A/(1+r)^0 0 -12,000 $(12,000.00) $(12,000.00) B B/(1+r)^1 1 1,500 $   1,376.15 $(10,623.85) C C/(1+r)^2 2 1,500 $   1,262.52 $ (9,361.33) D D/(1+r)^3 3 1,500 $   1,158.28 $ (8,203.06) E E/(1+r)^4 4 1,500 $   1,062.64 $ (7,140.42) F F/(1+r)^5 5 1,500 $      974.90 $ (6,165.52) G G/(1+r)^6 6 1,500 $      894.40 $ (5,271.12) H H/(1+r)^7 7 1,500 $      820.55 $ (4,450.57) I I/(1+r)^8 8 1,500 $      752.80 $ (3,697.77) J J/(1+r)^9 9 1,500 $      690.64 $ (3,007.13) K K/(1+r)^9 10 1,500 $      633.62 $ (2,373.51)

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.