Find the time required for an investment of 3,000 dollars to grow to 8,000 dollars at an interest rate of 7% per year, compounded monthly. Give your answer accurate to 2 decimal places.

Answer 1

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

where A = ending Amount = 8,000

P = starting Principle = 3,000

r= annual interest rate = 7% =.07

n = number of compounding periods annually = 12

8/3 = (1+ .07/12)^12t solve for t

2.666... = 1.0058333...^12t

use a calculator

log(8/3) to base 1.0058333... = 12t

t = (log(8/3)base 1.0058333...)/12 = (ln(8/3)/ln1.0058333...)/12

= ln(8/3)/12ln1.0058333...= about .98083/12(.00582)=

= about 14.05 years

check with

continuous compounding which is not that far from monthly

A =Pe^rt

8/3 =e^.07t

ln(8/3) = .07t

t= (ln8/3)/.07 = about 14.012 years

3000(1.0058333...)^12(14.01)

= 7976.16

3000(1.0058333...)^12(14.05)

= 7998.50

3000(1.0058333...)^12(14.06)

= 8004.09

Go with t= 14.05 years to reach 8,000 from 3000 at 7% compounded monthly