Finc

HOMEWORK #2 Due September 9, 2012

NAME: _________________________________

1. [20 points] Joanna’s dad is looking to deposit a sum of money immediately into an account that pays an annual interest rate of 9% so that her first year college tuition costs are provided for. Currently the average college tuition cost is $15,000 and is expected to increase by 4% (the average annual inflation rate). Joanna just turned 5, and is expected to start college when she turns 18.

a. [10 points] What will the average annual college tuition cost when Joanna turns 18 (i.e. the future compounded value of the current tuition cost)?

PV = –15,000;

n= 13;

i=4%;

PMT=0;

CPT FV=$24, 976.10 (rounded to 2 decimals)

FV = $15,000 × (1.04)13 = $15,000 × 1.66507 = $24,976.10

b. [10 points] How much money will Joanna’s dad have to deposit into the account? (Calculate the present value of the annual tuition cost)

FV = 24,976.10

n=13; i=9%

PMT = 0

CPT PV = $8,146.67 (rounded to 2 decimals)

PV = $24,976.10 × (1/(1+0.09)13 = $24,976.10 × 0.32618 = $8,146.67

2. [5 points] Your arch nemesis, who happens to be an accounting major, makes the following remark, “You finance types think you know it all…well, let’s see if you can tell me, without using a financial calculator, what rate of return would an investor have to earn in order to double $100 in 6 years?” How would you respond? (Rule of 72)

Use the rule of 72 to silence him once and for all and then prove the answer by compounding a sum of money at that rate for 6 years to show him how close your response was to the actual rate of return…Then ask him politely if he would like to borrow your jar of beans!

Rate of return required to double a sum of money = 72/N = 72/6 = 12%

Verification: $100(1.12)6 = $197.38…which is pretty close to double

The accurate answer would be calculated as follows:

PV = –100; FV = 200; n = 6; PMT = 0; I = 12.246%

OR

r = (FV/PV)1/n – 1 =...