ACTUARY Finance and Economics

Question 1

You invest $1,000 at an annual interest rate of 5% compounded annually. What will the investment be worth after 3 years?

Accepted Answer

$1,157.63

Answer

The formula for compound interest is:
FV=PV⋅(1+r) t
Here, PV=1,000, 𝑟=0.05 and t=3:

FV=1,000⋅(1+0.05) 3=1,000⋅(1.157625)=1,157.63

Question 2

What is the present value of $2,000 to be received 5 years from now if the annual discount rate is 6%?

Accepted Answer

$1,586.87

Answer

Here, FV=2,000, 𝑟=0.06, and t=5:
PV= 2,000/(1+0.06)5 = 2,000/1.338225 =1,586.87

Question 3

A bond with a face value of $1,000 pays annual coupons of $50 and has 4 years to maturity. If the market interest rate is 6%, what is the bond price?

Accepted Answer

$980.20

Answer

Total bond price:
𝑃𝑉total=173.26+792.94=980.20

Question 4

An investor has two assets in a portfolio:

Asset A: Expected return = 8%, weight = 60%
Asset B: Expected return = 12%, weight = 40%
What is the portfolio’s expected return?

Accepted Answer

10.4%

Answer

The portfolio's expected return is a weighted average of the asset returns:
E(R p​ )=w A​ ⋅R A+w RB

E(R p )=(0.6⋅0.08)+(0.4⋅0.12)=0.048+0.048=0.104=10.4%

Question 5

If the demand for a good increases and the supply remains unchanged, what happens to the equilibrium price and quantity?

Accepted Answer

Price increases, quantity increases

Answer

When demand increases and supply stays constant, the demand curve shifts to the right. This results in a higher equilibrium price and a larger equilibrium quantity. The market adjusts to the higher willingness of consumers to pay.

Actuary Certification Practice Test

Actuary Certification Practice Test

ACTUARY Finance and Economics