Use compound interest formula: A = P(1 + r)^t and the given information to solve for r

Question

The given information to solve for r are:

 

A = $4,000,000

 

P = $40,000

 

t = 40

 

Please help solve in step by step manner to determine the r.

Answer 1

For compound interest, r is in decimal form.  For example, at 4% interest, r would be 0.04.

 

With the equation A = P(1+r)^t

 

4,000,000 = 40,000(1+r)⁴⁰

4,000,000/40,000 = 100 = (1+r)⁴⁰

log(100) = log[(1+r)⁴⁰]

 

Now, using a property of logs:

log(100) = 40*log(1+r)

2 = 40*log(1+r)

2/40 = 0.05 = log(1+r)

10^0.05 = 1+r = 1.122018454

r = 0.12 or 12%

Answer 2

the underlying compound interest formula that you want to use to solve here is

A = P(1 + r)^n

for this scenario that means taking

4,000,000 = 40,000(1 + r)^40

4,000,000 / 40,000 = (1 + r)^40

100 = (1 + r)^40

r = 100^(1/40) - 1

r = 0.12202

which corresponds to an interest rate here of 12.20%