Question

30. You plan to purchase a home in x years. The goal is to have $50,000 as a down payment. In order to meet that goal, you invest in two zero coupon bonds. One zero coupon bond for face amount A matures in x-t years. A second zero coupon bond for face amount B matures in x+t years. You choose amount A and B such that the ability to make the $50,000 down payment in x years is immunized from changes in interest rates. Assume the force of interest is ?. Which of the following is a correct definition for A that meets the requirements for full immunization? A A = 25,000e$^{-t?}$ B A = 25,000e$^{t?}$ C A = 25,000 D A is a function of B E None of the above are correct definitions for A Question 31 During the first four years, interest is credited using a simple interest rate of 5% per year. After four years, interest is credited at a force of interest: $\delta_t = \frac{0.2}{1+0.2t}$, $t \ge 4$ The following are numerically equal: 1. the current value at time $t = 4$ of payments of 1,000 at time $t = 2$ and 400 at time $t = 7$; and 2. the present value at time $t = 0$ of a payment of X at time $t = 10$. Calculate X.

          30. You plan to purchase a home in x years. The goal is to have $50,000 as a down payment.
In order to meet that goal, you invest in two zero coupon bonds. One zero coupon bond
for face amount A matures in x-t years. A second zero coupon bond for face amount B
matures in x+t years.
You choose amount A and B such that the ability to make the $50,000 down payment in x
years is immunized from changes in interest rates.
Assume the force of interest is ?.
Which of the following is a correct definition for A that meets the requirements for full
immunization?
A
A = 25,000e$^{-t?}$
B
A = 25,000e$^{t?}$
C
A = 25,000
D
A is a function of B
E
None of the above are correct definitions for A
Question 31
During the first four years, interest is credited using a simple interest rate of 5% per year. After four years, interest is credited at a force
of interest:
$\delta_t = \frac{0.2}{1+0.2t}$, $t \ge 4$
The following are numerically equal:
1. the current value at time $t = 4$ of payments of 1,000 at time $t = 2$ and 400 at time $t = 7$; and
2. the present value at time $t = 0$ of a payment of X at time $t = 10$.
Calculate X.

30. You plan to purchase a home in x years. The goal is to have 50,000 as a down payment.
In order to meet that goal, you invest in two zero coupon bonds. One zero coupon bond
for face amount A matures in x-t years. A second zero coupon bond for face amount B
matures in x+t years.
You choose amount A and B such that the ability to make the50,000 down payment in x
years is immunized from changes in interest rates.
Assume the force of interest is ?.
Which of the following is a correct definition for A that meets the requirements for full
immunization?
A
A = 25,000e^-t?
B
A = 25,000e^t?
C
A = 25,000
D
A is a function of B
E
None of the above are correct definitions for A
Question 31
During the first four years, interest is credited using a simple interest rate of 5% per year. After four years, interest is credited at a force
of interest:
= (0.2)/(1+0.2t), t ≥ 4
The following are numerically equal:
1. the current value at time t = 4 of payments of 1,000 at time t = 2 and 400 at time t = 7; and
2. the present value at time t = 0 of a payment of X at time t = 10.
Calculate X.

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