Question

Homework #1 CIVE 240 ENGINEERING ECONOMICS 1- You have been paying $5000 every month for 6 years to a friend of yours who is extremely lazy to find a job. The annual interest rate is 9%, what is the worth of your money after 6 years with: a) Continuous compounding b) Every-six-months compounding 2- Suppose you open an account in a credit union. They have told you that the interest rate during each period is different. If you make three deposits at three different times (as shown in the cash flow diagram), what will be your balance at the end of the 5th year? What is the present value? F- 200 k 3- You are invited to a fancy birthday party and need new pants. You don't have the money to buy them and need $250. A true friend of yours offers to give you that money, only if you promise to repay him $270 after five months. What are the [annual] effective and nominal interest rates he is charging? Is she your true friend? 4 Your dad has a very generous uncle who finds you smart. He thinks if he gave you $7000 today, you can totally change your life with it. You tell him that you are going to invest that money in a saving account. He scratches his head, and tells you "Alright, return my 7000 once you earn $7000 of interest". Draw the cash flow diagram. If the interest rate is 18%, how long will he have to wait for his money?

Answer 1

Answer:

Given

Monthly Payment P=$5000

Number of Years = 6 years

Annual Interest Rate= 9%

A) Continuous Compounding

Number of Payment t= 6*12=72

monthly Interest rate r=9%/12=0.75%

FV=P*{(e^(r*t)-1)}/{(e^r-1)

FV=5000*{(e^(0.75%*72)-1)}/{(e^(0.75%)-1)}

FV=$475550.12

B) Every six month compounding

Then effective interest rate = (1+annual Interest rate/2)^2-1=(1+4.5%)^2=9.20%

So Monthly interest rate r=9.20%/12=0.77%

t=72

So FV= P*((1+r)^t -1 )/r=5000*((1+0.77%)^72 -1)/0.77%

FV=$478703.37