Compare the future amounts (A) you would have if the money were invested at simple interest and if it were invested with annual compounding.
$4,000 at 12% for 30 years
(a) Calculate the future amount if the money were invested at simple interest.
(b) Calculate the future amount if the money were invested with annual compounding. (Round your answer to the nearest cent.)
a. A = Po + Po*rt.
A = 4000 + 4000*0.12*30 = $18,400.
b. A = Po(1+r))^30
A = 4000(1,12)^30 = $119,839.69
To calculate the future amount for both scenarios, we need to use the formulas for simple interest and compound interest.
(a) Future amount with simple interest:
The formula for simple interest is: A = P(1 + rt)
Where:
A = Future amount
P = Principal amount (initial investment)
r = Interest rate (in decimal form)
t = Time period (in years)
Given:
P = $4,000
r = 12% = 0.12 (convert percent to decimal)
t = 30 years
Using the formula, we can calculate the future amount (A):
A = 4000(1 + 0.12*30)
A = 4000(1 + 3.6)
A = 4000 * 4.6
A = $18,400
So, the future amount with simple interest would be $18,400.
(b) Future amount with annual compounding:
The formula for compound interest is: A = P(1 + r/n)^(nt)
Where:
A = Future amount
P = Principal amount (initial investment)
r = Interest rate (in decimal form)
n = Number of times interest is compounded per year
t = Time period (in years)
Given:
P = $4,000
r = 12% = 0.12 (convert percent to decimal)
n = 1 (annual compounding)
t = 30 years
Using the formula, we can calculate the future amount (A):
A = 4000(1 + 0.12/1)^(1*30)
A = 4000(1 + 0.12)^(30)
A = 4000(1.12)^(30)
A = 4000 * 11.6284
A = $46,513.60
So, the future amount with annual compounding would be $46,513.60 (rounded to the nearest cent).