Question

1. If the interest rate is 4%, what are the proceeds of a $5,000 investment after 10 years?

?a) assuming simple interest

?b) assuming compound interest

2. What if interest in #1 is compounded semi-annually?  What if monthly?

3. How much do you need to deposit into a bank in order to receive proceeds of $200,000 in 5 years if the interest rate is 2.5%

What if interest is compounded quarterly?

4. What is the present value of $200,000 to be received in 5 years if the rate of discount is 2.5%?

5. What is the price today of a $200,000 cash flow in 5 years if the discount rate is 2.5%

6. What is the price today of $200,000 to be received in 6 years if the rate of discount is 2.5%?  Compare to #5.

7. What is the price today of $200,000 to be received in 5 years if the rate of discount is 3%?  Compare to #5.

8. Calculate the percentage price change between your answerin #5 and your answer in #7. This is known as the interest rate “sensitivity.”

Answer 1

1. a) Simple interest

Interest earned = 5,000*0.04*10 = 2,000

Total proceeds = 5,000 + 2,000

Total proceeds = $7,000

b) Compound interest

Total proceeds = 5,000 * 1.04^10

Total proceeds = $7,401.2214245917

2. Effective semi annual interest rate = 4%/2 = 2%

Now, we have 10 years or 20 semi-annual periods

So, total proceeds = 5,000 * 1.02^20

Total proceeds = $7,429.7369798918

Effective monthly interest rate = 4%/12 = 0.3333333333%

Total proceeds = 5,000*1.003333333333^(12*10)

Total proceeds = $7,454.1634117941

3. PV = FV/(1+r)^5

PV = 200,000/(1 + 0.02)^5

PV = $181,146.161965983

So, if you deposit $181,146.161965983 today at 2% interest rate, it will grow to $200,000 in 5 years

If the interest rate is compounded quarterly, then the effective interest rate is 2%/4 = 0.5% per quarter

We have 5 * 4 = 20 quarters

PV = 200,000/(1 + 0.005)^20

PV = $181,012.58085333

Note that we can deposit less if the interest rate is compounded quarterly to get the same payout of $200,000 in 5 years.

4. PV = 200,000/ (1 + 0.025)^5

PV = $176,770.857521903

5. Price today = 200,000/ (1 + 0.025)^5

Price today = $176,770.857521903

6. Price today = 200,000/ (1 + 0.025)^6

Price today  = $172,459.373192101

This price is lower because we are receiving the same cash flow but one year later as compared to the cash flow we received in Q5

7. Price today = 200,000/(1 + 0.03)^5

Price today = $172,521.756876833

This price is lower because the interest rate is higher than in Q5.

8. Sensitivity = 172,521.756876833/176,770.857521903 - 1

Sensitivity = -0.02403733684

Sensitivity = -2.403733684%

Can you please upvote? Thank You :-)