Question

The present value of K due in 2 years is 678.80. If the force of discount (same as force of interest ) is cut by a factor of 1/4, that present value would be 766.30. What would the present value be if the rate of discount d is cut by a factor of 1/5?

Answer 1

In case of force of interest the interest rate are compounds continuously. The equation below shows the relationship between Present value (PV), Future Value(FV) and force of interest (d)
PV * e^(yd) = FV    ---->(1)

Here y is the number of years.

Or, 678.80 *e^(2*d) = FV ---à(2)

Or, 766.30 *e ^(2* 0.75d) = FV

Or, 678.80 *e^(2*d) = 766.30 *e ^(2* 0.75d)

Or, e^(2*i)/e^(1.5d) = 766.30/678.80

Or, e^(0.5 d) = 1.12890395

Or, 0.5 *d = ln(1.12890395)

Or, d= 0.242494412          ----à(3)

Or, FV = 678.80* e^ (2*0.242494412) (From equation 2 and 3)

Or, FV = 1102.47767

Present value be if the rate of discount d is cut by a factor of 1/5

Or, 1102.47767 = PV * e^(2* 0.242494412*0.8)

Or, 747.94115 = PV