Question

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%.

3. 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%.

4. If you invest your money would you rather get 5% compounded quarterly or 5.10% compounded annually?

5. What is the effective annual interest rate of 8.25% compounded semiannually?

6. 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?
7. 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?
8. 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.

9. 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.

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.