Question

Compounding - solve for time Elijah invested $610 in an account paying an interest rate of 4.1% compoundedannually. Assuming no deposits or withdrawals are made, how long would it take, to the nearest year, for the value of the account to reach $900?

Answer 1

Principal amount invested = P=$610

Interest rate =r= 4.1 % = 4.1/100 = 0.041 (decimal form)

Apply the compound interest formula:

A = P (1+r)^t

Where;

A = future value of investment = $900

t = years

Replace:

900 = 610 (1+0.041)^t

Solve for t:

900/610 = (1+0.041)^t

90/61 = 1.041^t

Ln (90/61) = Ln (1.041)^t

Ln (90/61) = t (Ln (1.041))

Ln (90/61) / ln (1.041) = t

t = 9.67 years = 10 years