Question

Please show work!

Would you rather have $3,000 today or $5,000 in 5 years if your opportunity cost of capital is 10%?

How much do you have to invest today to have $15,000 in 3 years if you can get 9% return on your investment?

Would you pay someone $10,000 today in order to get $19,000 in 10 years if your opportunity cost of capital is 9%?

What is the effective annual interest rate of 7.25% compounded quarterly?

How much do you need in the bank when you retire if you would like to withdraw $200,000 each year for the 30 years that you are retired? You can get an 8% return on your investment.

If you invest $7,500 each year from now until you retire (for 40 years) how much will you have in 40years? Your return will be 8%.

Would you pay someone $25,000 today to get $5,000 each year for the next 7 years? You can get a return on your invested money of 10%.

What is your house payment if you buy a house for $250,000, put 20% down and finance the rest for 30 years at 3.95%?

What is your car payment if you buy a car for $27,000, put 10% down and finance the rest for 3 years at 6.25%?

If you leave the Animal Shelter $35,000 when you die, how much can they take out each year forever if they get a return of 7% on their investments?

Answer 1

QUESTION NO. 1

We can choose by calculating Present value.

Option 1.

Present Value=  $3000

Option 2

Present Value = $5000 * PVF(10%, 5 Years) = $5000 * 0.621 = $3105

Since in Option 2, Receipt amount is greater, so, option 2 is better.

QUESTION. 2

Future Value = $15000

Interest Rate= 9% p.a.

Number of years = 3

We have to calculate Present value, that can be calculated as follows:-

$15000 = PV * (1+ 9%)^3

$15000 = PV * 1.09^3

$15000 = PV * 1.295029

PV = $11582.75

I.e, we have to invest $11582.75 today.

QUESTION 3

Future Value of $10000 after 10 Years @ 9% p.a.

= $10000 * (1+9%)^10 = $10000 * 1.09^10 = $10000 * 2.3674 = $23674

Since the maturity amount of Investment is lower than $23674 (as per our opportunity cost), so, we should not invest $10000 to get $19000 after 10Years.

Question 4

Effetctive Annual Interest Rate = (1 + i/n)^n - 1

where i= annual Interest Rate and n = number of compounding periods

i = 7.25% / 100 = 0.0725 and n = 4 (compounding quarterely)

so,

Effetctive Annual Interest Rate = (1 + 0.0725/4 )^4 - 1

= ( 1 + 0.018125)^4 - 1 = (1.018125)^4 - 1 = 1.0745 - 1 = 0.0745 = 7.45%