Question

How long will it take for $470 to grow to $1,700 at the following interest rates? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

4.7%

8.7%

16.7%

Answer 1

Assumption: The interest rate is compounding interest rate paid annually.

a) i = 4.7%

A= P(1+r)^n

1700 = 470* (1+ 0.047)^n

3.617 = 1.047^n

taking log both side

Log (3.617) = Log (1.047)^n

Log (3.617) = n* Log (1.047)

n = log (3.617)/log(1.047)

n= 0.558/0.0199

n= 28.04 or 28.04 years

B) i = 8.7%

A= P(1+r)^n

1700 = 470* (1+ 0.087)^n

3.617 = 1.087^n

taking log both side

Log (3.617) = Log (1.087)^n

Log (3.617) = n* Log (1.087)

n = log (3.617)/log(1.087)

n= 0.558/0.036

n= 15.52 or 15.52 years

C) i =16.7%

A= P(1+r)^n

1700 = 470* (1+ 0.167)^n

3.617 = 1.167^n

taking log both side

Log (3.617) = Log (1.167)^n

Log (3.617) = n* Log (1.167)

n = log (3.617)/log(1.167)

n= 0.558/0.067

n= 8.32 or 8.32 years