Please help me College Algebra

Question

Use A=P(1+r/n)^nt  where:A = the amortized amount (total loan/investment amount over the life of the loan/investment)P = the initial amount of the loan/investmentr = the annual rate of interestn = the number of times interest is compounded each year t = the time in years Find how long it takes a $2,500.00 investment to earn $280.00 in interest if it is invested at 6% compounded annually.

It will take years. (Round answer to 3 decimal places.)

The answer I keep getting is around t=1.8835 rounded 3 decimal places which makes my answer 1.884. Apparently my answer is wrong and i honestly don't know what to do. Help please

Answer 1

First, let's simplify that equation: "compounded annually" means n = 1, so

A = P * (1+r)^t

Let's solve for t now:

A/P = (1+r)^t

ln(A/P) = t * ln(1+r)

t = ln(A/P)/ln(1+r)

And substitute the rest of the known values:

A = 2500 + 280

t = ln(2780/2500)/ln(1.06)