Question

QUESTION 1 At an interest rate of 3%, what comes closest to the amount of time it takes for a deposit of $7,500 to reach $15,000? O a. 11.90 years b. 14.21 years c. 23.45 years d. 10.24 years e. 17.67 years QUESTION 2 You are trying to price two bonds that have the same maturity and par value but different coupon rates. Both bonds mature in 8 years and at maturity both bonds return the par value of $1,000. One bond has a coupon rate of 3% and a yield to maturity of 3%. The other bond has a coupon rate of 5% and a yield to maturity of 3%. What is the absolute value of the difference between the prices of these two bonds? a. $ 140.39 b. $ 67.33 c. $ 119.43 d. $0 e. $ 62.10 QUESTION 3 If $400 grows to $4,000 in 7 years, approximately what interest rate is earned? a. 33% b.26% C. 39% d. 23% O e. 29%

Answer 1

Question 1:

Given, interest rate, r = 3%.

Initial amount, P₀ = $7,500.

Final amount, P_n = $15,000.

We know that P₀ becomes P_n in n years by compounding formula: P_n = P₀ * ( 1 + r% )ⁿ

Where, n is the number of years.

=> 15,000 = 7,500 * (1+0.03)ⁿ

=> 2= (1.03)ⁿ

Applying logarithm on both sides,

=> log2 = log (1.03)ⁿ

=> log2 = n * log(1.03)

=> n = log2 / log(1.03)

=> n = 0.3 / 0.0128

=> n = 23.45 years.

Answer is (c).

Question 2:

Let, Coupon rate = r^*

Yield To Maturity = YTM

Redeemable value = RV = Par value

n = Maturity period

Sale Price = SV

Two bonds maturity period of 8 years and return par value of $1,000.

Bond 1:

n = 8; RV = $1,000; r^*= 3%; YTM = 3%

Bond 2:

n = 8; RV = $1,000; r^* = 5%; YTM = 3%

Approximate Formula for YTM: YTM = ( I + { RV - SV } / n) / (0.6 RV + 0.4 SV)

Where, I = Interest rate = par value * coupon rate.

All the calculations are shown in the below image:

Tim. It (Rw=su) Apponimale formula 6.6 Ruftsv). Here. , Iulisest sale Boudt :- I pas value & Coupon haté z1,0000.03 = 30$ » 0.03 30+ (1000 - su) (0.6% 1000 +0.4% sv) ») 003(600+ 0.4 sv) - 30+ (125-011155V) > 18 +0.012 SV = 155-0.125 SV >> 0.01375V = 137 > SV = 137 - $1,000 0.0137 I. 1,000 * 0.05-50$ Bondz - >> 0.03 = 50+ / 1000 —5V 8 s 70.6x1000+04 sv) 18+ 0.012 SV - 50+ (125 -0.125 5v) >> 0.1375V= 175-18 = 157 ») Sv: 157 . $1145.99 0.137
The price of Bond 1 = $1,000

The price of Bond 2 = $1,145.99

Therefore, the difference between absolute values = 1,145.99 - 1,000 = $145.99

As this is approximate value, it is closer to option (a) i.e., 140.39.

Therefore, answer is option (a).

Question 3:

Given, Initial amount P₀ = $400.

Final amount, P_n = $4,000.

Number of years, n = 7 years.

Let, r is the interest rate.

We know that, P_n = P₀ * ( 1 + r% )ⁿ

=> 4,000 = 400 * (1+r)⁷

=> 4,000/400 = (1+r)⁷

=> 10 = (1+r)⁷

=> 10^1/7 = 1+r

=> 1.39 = 1+r

=> 1.39 - 1 = r

=> r = 0.39 or 39%.

Answer is (c).