Question

PLEASE SHOW ALL WORK. Thanks! How much will you have when you retire if you save...

PLEASE SHOW ALL WORK. Thanks!

  1. How much will you have when you retire if you save $8,000 each year for 45 years? Your average return will be 8%.
  2. Would you rather get $20,000 today or $2,000 at the end of each year for 15 years? Your opportunity cost of capital is 8%.
  1. Would you rather get $15,000 in 10 years or 1,000 at the end of each year for 10 years? Your opportunity cost of capital is 12%.
  1. If you invest your money would you rather get 5% compounded quarterly or 5.10% compounded annually?
  1. What is the effective annual interest rate of 8.25% compounded semiannually?
  1. What would your car payment be if you purchased a $24,000 car, put 10% down and financed the balance at 5.25% for three years?
  2. What would your house payment be if you purchased a $180,000 house, put 20% down and financed the balance at 3.75% for 30 years?
  3. If you leave the Humane Society $25,000 how much can they spend each year forever?   The HS can get a return of 4% on their investments.
  1. If you would like to give a scholarship for $3,000 each year forever how much do you need to leave WCU? The investment will get a 5% return.

Homework Answers

Answer #1

As per rules I am answering the first 4 subparts of the question

1: Future Value of annuity = A* ((1+rate)^n-1)/rate

= 8000*(1.08^45-1)/0.08

=3092044.94

2: PV of annuity = Annuity*(1-1/(1+rate)^number of terms)/rate

= 2000*(1-1/1.08^15)/0.08

=17118.96

It is better to receive $20,000 now since that amount is greater.

3: Future Value of annuity = A* ((1+rate)^n-1)/rate

= 1000*((1+0.12)^10-1)/0.12

=17548.74

It is better to get the annity since it is higher than the amount of $15000 received in 10 years.

4: for determining this we need to calculate the effective rate of interest

EAR= (1+APR/m)^m-1

Option 1 EAR = (1+0.05/4)^4-1= 5.09%

This is lesser than option 2 and hence it will be more beneficial to receive 5.1% annually.

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