Question

What is the present value of $100 ten years from now if the simple rate of interest is0.12? Round your final answer to two decimal places. Question 2 2 pts A deposit of $19 is made at the beginning of each year for 14 years, what is the future value of all deposits if simple rate of interest is 0.09? Round your final answer to two decimal places. Question 3 2 pts In how many years will $100 become $320 if simple rate of interest is 11%? 20

Answer 1

Future value of simple interest is given by the formula, F = P * [ 1+ (rt) ] where

F = Future Value = Principal + Simple Interest

P = Principal invested now for t years at r% simple interest.

Question 1

Given

F = $100; t = 10 years; r = 12% p.a

Substituting values,

$100 = P * [ 1 + ( 0.12 * 10 ) ]

$100 = P * [ 1 + (1.2) ]

$100 = P * [ 2.2 ]

P = $100 / 2.2 = $45.45

Answer1: Present value amount invested = $45.45

Question 2:

Future value of all deposits made $19 p.a at the beginning of the year, simple interest 9% for 14 years.

Given:

• Annual deposit at the beginning of the year = $19
• Simple interest rate = 9%
• Investment duration = 14 years
  • Future Value of 1st $19, invested for 14 years, FV0 = P * [ 1 + (rt) ] = $19 * [ 1 + 0.09 * 14) ] = $42.94
  • Future Value of 2nd $19, invested for 13 years, FV1 = P * [ 1 + (rt) ] = $19 * [ 1 + 0.09 * 13) ] = $41.23
  • Future Value of 3rd $19, invested for 12 years, FV2= P * [ 1 + (rt) ] = $19 * [ 1 + 0.09 * 12) ] = $39.52
  • Similar calculation for remaining years
  • Future Value of 14th $19, invested for 1 year, FV13 = P * [ 1 + (rt) ] = $19 * [ 1 + 0.09 * 12) ] = $20.71

Future value is the sum of all the 14 $19p.a investment = FV0 + FV1 + ...+ FV13 = $445.55

Answer2: Future value = $445.55

Question3:

In how many years $100 will become $320 at 11% simple interest rate?

Given: FV = $320; P = $100; r = 11%

to find: t

Using values, $320 = $100 * [ 1+ ( 0.11 * t) ]

• $320 / $100 = [ 1 + ( 0.11 * t ) ]
• [ 1 + ( 0.11 * t ) ] = 3.2
• 0.11 * t = 3.2 - 1
• 0.11 * t = 2.2
• t = 2.2 / 0.11
• t = 20 years

Answer3: In 20 years, $100 will become $320 at 11% simple interest rate.