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Question

Find how long it takes $1500 to double if it is invested at 6% interest compounded semiannually. Use the formula 

 

A=P ( 1 + R/N)nt  to solve the compound interest problem

 

it will take approximately years??????

Answer 1

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

 

We want the investment to double, so that A = 2P.  We also know that r = 0.06 (6% as a decimal value), n=2 (semi-annual).  We need to solve for t, the number of years needed to double the investment.

 

2P = P(1 + (0.06/2))^2t

 

2 = (1.03)^2t                          [Combined terms and divided both sides by P]

 

To get the t out of the exponent, take the log.  I'll use ln (natural log) but you can use log₁₀ or any other base log:

 

ln(2) = 2t ln(1.03)                    [ln(1.03)^2t = 2tln(1.03)]

 

ln(2)/2ln(1.03) = t                   [Use a calculator to compute the logs (ln)]

 

11.72 = t ≈ 12 years