find the time required for an investigation of 1 dollars to grow to 6500 dollars at an interest rate of 7.5 percent per year, compounded quarterly

Question

find the time required for an investigation of 1 dollars to grow to 6500 dollars at an interest rate of 7.5 percent per year, compounded quarterly

 

Answer 1

Hi Sam,

 

Recall the equation for compound interest

 

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

Where 

A = final value (accumulated value)

P = principal (amount invested)

i = annual interest rate, expressed as a decimal

n = frequency of compounding

t = # years

 

Let's plug in what we know

6500 = 1(1+.075/4)^4t

6500 = 1.01875^4t

 

We need to take the natural log (ln) to be able to solve for t

 

ln 6500 = 4t ln 1.01875

 

8.779557 = 4t (.01857638557)

 

472.62 = 4t

t = 118.15

 

It will take over 118 years.

Answer 2

First, let's substitute investment for your word investigation.  Also, don't say 1 dollars because it's not plural.

 

Now, to the Math. We use A(t) = 1(1+0.075/4)^4t where A(t) is to be 6500 at the end of t years.  So we must solve

6500 = 1.01875^4t.  To solve this, we must take logarithms:

 

ln 65000 = 4t•ln1.01875 from which we get t = 118.15 years.

 

So my advice is don't try this at home because you''ll probably not live that long!