Madhubala Devi purchased one or more of the 5 available bonds from her bonus pay and spent the remainder. She made the purchase decision such thather return from the bonds is maximized. Her return
from the bonds is

Let the coupon payments of A, E, B, D and C be a-2d, a-d, a, a+d, and a+2d, respectively.

Since, the coupon payment of A is twice the common difference,

a - 2d = 2d

a = 4d

Thus, the coupon payments of A, E, B, D and C are 2d, 3d, 4d, 5d, and 6d, respectively.

Since the coupon payment on bond B is half the price of bond A, the price of bond A = 2 x 4d = 8d.

Let the price of bond E be $$x$$. Thus, the price of bond B = $$1.75x$$.

Let the face value of bond E be $$e$$. Thus, the face value of bond B = $$2e$$.

Since the face value of bond C is equal to the price of bond A, the face value of C is 8d.

We know that three of the bonds mature in two years, two in three years and one in five years. We are also given that A matures in 2 and D matures in 5 years.

Tabulating the given information.

Applying the price formula for A, we get

8d = $$\frac{2d}{1.25}+\frac{2d}{1.25^2}+\frac{1000}{1.25^2}$$

Solving this, we get $$d=125$$

Thus, the coupon payments of A, B, C, D, and E are 125, 500, 750, 625 and 375, respectively.

Price of A = 8d = 1000 = Face value of C

We are given that the price of bond C is more than 1800. The time period for C could be 2 or 3 years.

Case 1: Time period is 2 years.

Applying the price formula for C.

Price = $$\frac{750}{1.25}+\frac{750}{1.25^2}+\frac{1000}{1.25^2}$$

Price = 1720 (<1800)

Thus, the maturity period of bond C is 3 years and for bonds B and E will be 2 years.

Applying the price formula again, we get

Price = $$\frac{750}{1.25}+\frac{750}{1.25^2}+\frac{750}{1.25^3}+\frac{1000}{1.25^3}$$

Price of C = 1976

Using the price formula on bond B, we get

1.75$$x$$ = $$\frac{500}{1.25}+\frac{500}{1.25^2}+\frac{2e}{1.25^2}$$ ...(1)

Using the price formula on bond E, we get

$$x$$ = $$\frac{375}{1.25}+\frac{375}{1.25^2}+\frac{2}{1.25^2}$$ ...(2)

Solving equations (1) and (2) simultaneously, we get

$$x=1440$$ and $$e=1406.25$$

Thus, the table becomes

Since Madhubala has Rs. 2500, she can either buy one bond each of A and E, or a single bond C.

Return from bonds A and E = 1000 + 2(250) + 1406.25 + 2(375) = 3656.25

Return from bond C = 1000 + 3(750) = 3250

Thus, the maximum return that Madhubala can get is Rs. 3656.25.

Hence, the answer is option C.