How long will it take for a $16000.00 investment to grow to $20000.00 if it is invested at a 4% annual simple interest rate?

Question

How long will it take for a $16000.00 investment to grow to $20000.00 if it is invested at a 4% annual simple interest rate?

Answer 1

A = amount after t years

P = original investment

r = interest rate (in decimal form)

n = number of times interest is compounded per year

 

A = P(1 + r/n)^nt

 

20000  = 16000(1 + 0.04/1)^(1)(t)

 

1.25 = (1.04)^t

 

log(1.25) = log(1.04)^t

 

log(1.25) = t[log(1.04)]

 

t = log(1.25)/log(1.04)  ≈ 5.69 years 

Answer 2

 

General equation: interest = (principal)(interest rate)(time)

 

Given: 

Principal = 16,000

Interest rate = 4% or 4/100 which is 0.04

Interest = 20,000-16,000 = 4,000

Time = unknown (what you need to solve for). Call time t

 

Plug given into the general equation:

4,000 = 16,000(0.04)t

 

Rewrite:

4,000 = 640t

 

Solve for t by dividing both sides by 640 

t = 6.25 or 6 years and 3 months

 

Answer: 6.25 or 6 years and 3 months