Answer:
a. To have $66,000 in four years with an annual interest rate of 9%, the present value is:
PV = $66,000 x discount factor
= $66,000 x (1.09)^4
= $66,000 x 0.708
= $46,728
b. To have $18,500 in two years with an interest rate of 8% yearly, the present value is:
PV = $18,500 x discount factor
= $18,500 x (1.08)^2
= $18,500 x 0.857
= $15,854.50
c. The future value of an investment of $787 for ten years earning an interest of 9% is:
FV = $787 x FV factor
= $787 x (1.09)^10
= $787 x 2.367
= $1,862.83
Explanation:
The present values for options A and B are calculated by discounting the future values with their discount factors. The present values show the amounts that need to be invested today at prevailing interest rates to yield the future values after the indicated periods of time.
The future value for option C is calculated by multiplying the present value of the investment with its future value factor. These present and future values show that there is a time value of money. This concept means that money received today is not equal in value to the same amount received some time later. Based on this difference, interest rates are charged to equate the values of money received today and money received in a year's time. The interest rates also consider the inflation rate and must always be above the inflation rate in order to retain future value.
