# 1. Solve the following questio

1. Solve the following questions.

a) Suppose Rosie’s mum is considering purchasing a financialasset that promises to pay $2,500 per year for six years, with thefirst payment one year from now. The required return is 11% peryear. How much should Rosie’s mum pay for this asset?

b) For the year 2000, Coca-Cola Company, recorded net sales of$7,368 million. For 2010, Coca-Cola recorded net sales of $11,245million. Over the ten-year period from the end of fiscal year 2000to the end of 2010, What is the Coca-Cola’s growth rate?

c) Leo is planning to purchase a home for $550,000 inCharleston, SC. He intends making a down payment of $50,000 andborrowing the remaining amount with a 30-year fixed rate mortgagewith monthly payments. The first payment is due a month from now.The current mortgage rates are quoted at 4% per year with a monthlycompounding. How much would Leo’s monthly mortgage payment be?

d) Clementine is the lucky winner of the Georgia lottery of $50million after taxes. He invests his winnings in a 10-yearcertificate of deposit (CD) at the Lawrenceville Credit Union. TheCD promises to pay 6% per year, compounded quarterly. The creditunion allows investors to reinvest the interest at that rate forthe duration of the CD. How much will Clementine have at the end often years if his money remains invested at 6% for ten years with nowithdrawals?

e) Caillou is interested in determining how long it will take aninvestment of $20,000 to double. The current interest rate is aninterest rate of 10%?

Answer:

**QUESTION 1**

This is basically an ordinary annuity, which pays $2,500 peryear for 6 years for which we need to calculate the presentvalue.

Present value of an annuity is mathematically representedas:

For our question, P = $2,500 r = 11%, n = 6 years, and we needto calculate PV.

Hence, substituting values, we get:

PV (or amount to be paid by Rose’s mum) = **$10,576.34**

**QUESTION 2**

This question requires application of basic time value of moneyfunction, according to which:

FV = PV * (1 + r)^{n}

11,245 = 7,368 * (1 + r)^{10}

(1 + r)^{10} = 1.5262

(1 + r) = 1.0432

**r =4.32%**

**QUESTION 3**

This again is an example of present value of an annuity.However, here the annuity payments are monthly.

Again for application of mathematical relation in Q.1, let usdefine the inputs.

PV = $550,000 – $50,000 = $500,000

N = 30 years * 12 months = 360 months

R = 4% per year = 0.33% per month

We need to calculate the value of P.

Substituting values in our mathematical relation, we get:

**P =$2,387.08** — > Monthly payment for loan servicing

**QUESTION 4**

This question requires application of basic time value of moneyfunction, according to which:

FV = PV * (1 + r)^{n}

PV = $50 mil

R = 6%/4 = 1.5% per quarter

N = 10 years * 4 quarters = 40 quarters

FV = 50 * (1 + 0.015)^{40}

**FV = $90.70mil**

**QUESTION 5**

We will again use basic TVM function here to calculate n:

40000 = 20000 * (1 + 10%)^{n}

2 = (1.1)^{n}

Taking log on both sides

ln (2) = n ln (1.1)

**n = 7.27 years**

It would take 7.27 years to double the invested amount at 10%per annum.