Question

My Notes Ask Your Teacher Business and finance texts refer to the value of an investment at a future time as its future value. If an investment of P dollars is compounded yearly at an interest rate of ras a decimal, then the value of the Investment after t years is given by the formula below. Future value - Px (1 + r) In this formula, (1 + r)' is better known as the future value interest factor, so the formula above can also be written as the formula below. Future value = P x Future value interest factor Financial officers normally calculate this (or look it up in a table) first. (a) What future value interest factor will make an investment double? Triple? double investment triple investment b) Say you have an investment which is compounded yearly at a rate of 9%. Find the future value interest factor for a 9-year investment. (Round your answer to two decimal places.) 2 17 (c) Use the results from part (b) to calculate the 9-year future value if your initial investment is $6,000.

Answer 1

Future value= P * (1 + r)^t   (Given)

Future value= P * Future value interest factor (Given)

Future value interest Factor = (1 + r) ^t (Given)

(a) Double Investment

Future value interest factor which make an investment double =

  Future value= P * (1 + r)^t

Since the investment to be double , Future value = 2P

ie, 2P = P * future value interest factor

= Future value interest factor = 2P/P

= Future value interest factor = 2

Triple Investment

Future value interest factor which make an investment triple =

  Future value= P * (1 + r)^t

Since the investment to be triple , Future value = 3P

ie, 3P = P * future value interest factor

= Future value interest factor = 3P/P

= Future value interest factor = 3

(b)Future value interest factor for a 9 year investment; interest rate =9%

Future value interest Factor = (1 + r) ^t (Given)

= (1+ 0.09) ⁹

= (1.09) ⁹

= 2.17189

= 2.17(rounded)

(c)Computation of 9 year future value if your initial investment is $6000

Future value= P * Future value interest factor (Given)

here P = $6000

Future value interest factor = 2.17 (results from part b)

Future value = $6000 * 2.17

= $13020