Question

The face value of bond E must be:

• A. Rs. 1406.25
• B. Rs. 1686.25
• C. Rs. 2250.50
• D. Rs. 2812.50
• E. Rs. 3372.50
• A. Rs. 3000.00
• B. Rs. 3250.00
• C. Rs. 3656.25
• D. Rs. 3906.25
• J. Rs. 4531.25
• A. Rs. 1825
• B. Rs. 1874
• C. Rs. 1925
• D. Rs. 1976
• O. Rs. 2342

Answer 1

The Correct Option is A

Step 1: Recall the bond pricing formula.
The price of a bond is given as the present value of all future coupon payments plus the present value of the face value. In other words, \[ P = \left[ \frac{C}{(1+R)} + \frac{C}{(1+R)^2} + \ldots + \frac{C}{(1+R)^T} \right] + \frac{F}{(1+R)^T} \] where $P$ = Price of bond, $C$ = Annual coupon payment, $F$ = Face value, $T$ = Years to maturity, $R = 0.25$ (25 percent). Step 2: Use given information.
- Coupon payments are in arithmetic progression: A, E, B, D, C.
- Coupon on A = 2d, on B = 4d, on C = 6d, on D = 5d, on E = 3d.
- Face value of A = 1000.
- Face value of B = 2 × Face value of E.
- Price of B = 1.75 × Price of E.
- Face value of C = Price of A.
- Price of C is greater than 1800.
- Bond A matures in 2 years.
- Bond D matures in 5 years.
- One of the bonds matures in 3 years, while two others mature in 2 years.
- Bond D has the largest face value.
Step 3: Solve for coupon size d.
Using Bond A:
Coupon payment = 2d.
Price = 1000.
Maturity = 2 years.
So,
1000 = (2d)/(1.25) + (2d)/(1.25)^2 + (1000)/(1.25)^2.
Simplify this expression step by step:
(2d/1.25) = 1.6d.
(2d)/(1.25^2) = 1.28d.
(1000)/(1.25^2) = 640.
Therefore,
1000 = 1.6d + 1.28d + 640.
1000 − 640 = 2.88d.
360 = 2.88d.
d = 125.
Thus coupon payments are:
A = 250, B = 500, C = 750, D = 625, E = 375.
Step 4: Verify Bond C’s maturity.
If Bond C matures in 2 years, its price will be less than 1800. But we know it is greater than 1800. Therefore Bond C must mature in 3 years.
Price of C with T = 3 years:
= (750)/(1.25) + (750)/(1.25^2) + (750)/(1.25^3) + (1000)/(1.25^3).
= 600 + 480 + 384 + 512.
= 1976, which is indeed greater than 1800.
So maturity of C = 3 years.
Step 5: Apply given relation between B and E.
We know Price of B = 1.75 × Price of E.
Also, Face value of B = 2 × Face value of E.
Step 6: Use pricing formula for B.
Coupon on B = 500.
Maturity of B = 2 years.
Price of B = (500)/(1.25) + (500)/(1.25^2) + (Face value of B)/(1.25^2).
Let Face value of E = e. Then Face value of B = 2e.
So Price of B = 400 + 320 + (2e)/1.5625.
But Price of B = 1.75 × Price of E.
Step 7: Use pricing formula for E.
Coupon on E = 375.
Maturity = 2 years.
Price of E = (375)/(1.25) + (375)/(1.25^2) + (e)/(1.25^2).
= 300 + 240 + e/1.5625.
Step 8: Set up equations.
Price of B = 400 + 320 + (2e)/1.5625.
Price of E = 540 + e/1.5625.
Now, Price of B = 1.75 × Price of E.
So,
720 + (2e)/1.5625 = 1.75 × [540 + e/1.5625].
Step 9: Simplify.
Left-hand side = 720 + 1.28e.
Right-hand side = 945 + 1.12e.
So equation becomes:
720 + 1.28e = 945 + 1.12e.
Simplify:
1.28e − 1.12e = 945 − 720.
0.16e = 225.
e = 225 ÷ 0.16 = 1406.25.
Step 10: Conclude.
Therefore, the face value of Bond E is Rs. 1406.25. \[ \boxed{1406.25 \; \text{(Option A)}} \]

Answer 2

Step 1: Recall her budget.
Madhubala Devi received Rs. 2500 as Diwali bonus. She can purchase one or more bonds, but the cost cannot exceed Rs. 2500.
Step 2: Recall bond details (from earlier calculation). \[ \begin{array}{|c|c|c|c|c|c|} \hline & A & B & C & D & E
\hline \text{Coupon Payment} & 250 & 500 & 750 & 625 & 375
\hline \text{Price} & 1000 & 2520 & 1976 & - & 1440
\hline \text{Face Value} & 1000 & 2812.5 & 1000 & - & 1406.25
\hline \text{Years to Maturity} & 2 & 2 & 3 & 5 & 2
\hline \end{array} \] Note: Bond D is omitted here because its price is too high compared to Madhubala’s budget of Rs. 2500.
Step 3: Possible purchase combinations.
- Option 1: Buy Bond C.
Price of Bond C = Rs. 1976, which is within her budget of Rs. 2500.
Return from Bond C = Face Value + Total Coupon Payments.
= 1000 + (3 × 750).
= 1000 + 2250.
= Rs. 3250.
- Option 2: Buy Bonds A and E together.
Price of A = 1000, Price of E = 1440. Total = 2440 (within budget).
Return = (Face Value of A + Coupons from A) + (Face Value of E + Coupons from E).
For Bond A: Return = 1000 + (2 × 250) = 1000 + 500 = 1500.
For Bond E: Return = 1406.25 + (2 × 375) = 1406.25 + 750 = 2156.25.
Total return = 1500 + 2156.25 = Rs. 3656.25.
- Option 3: Try other combinations.
Bond B costs Rs. 2520, which exceeds her budget of Rs. 2500. So it cannot be bought.
Bond D also costs more than Rs. 2500, so it cannot be bought either.
Thus, only the above two options are feasible.
Step 4: Compare returns.
Return from Bond C alone = Rs. 3250.
Return from Bonds A + E together = Rs. 3656.25.
Clearly, the second option gives the higher return.
Step 5: Conclude.
Therefore, Madhubala Devi should buy Bonds A and E to maximize her return, which equals Rs. 3656.25. \[ \boxed{3656.25 \; \text{(Option C)}} \]

Answer 3

Step 1: Recall bond price formula.
Price of a bond is equal to the present value of all coupon payments plus the present value of its face value. That is: \[ P = \left[ \frac{C}{(1+R)} + \frac{C}{(1+R)^2} + \ldots + \frac{C}{(1+R)^T} \right] + \frac{F}{(1+R)^T} \] where $C$ = coupon payment, $F$ = face value, $T$ = maturity years, $R = 0.25$ (25 percent).
Step 2: Values from previous derivation.
We had already determined that $d = 125$.
Thus coupon payments are:
A = 250, B = 500, C = 750, D = 625, E = 375.
Face values: A = 1000, C = 1000, E = 1406.25, B = 2812.5, D largest (not needed here).
Step 3: Test possible maturity for Bond C.
It was given that Price of Bond C is more than 1800.
So we must check whether its maturity is 2 years or 3 years.
- If maturity = 2 years:
Price = (750)/(1.25) + (750)/(1.25^2) + (1000)/(1.25^2).
= 600 + 480 + 640 = 1720.
Since this is less than 1800, it cannot be correct.
- If maturity = 3 years:
Price = (750)/(1.25) + (750)/(1.25^2) + (750)/(1.25^3) + (1000)/(1.25^3).
= 600 + 480 + 384 + 512.
= 1976.
Step 4: Conclude.
Since the 3-year maturity gives price greater than 1800 and equal to 1976, this is the correct price of Bond C. \[ \boxed{1976 \; \text{(Option D)}} \]