Joe has $1,800 from his summer job to invest. if Joe wants to have $2,340 altogether and invests the money at 5% simple interest, in how many years will be have $2,340?

In economics, the formula relating the future value (F) and present value (P) at simple interest (i) and number of years (n) is:

F = P (1 + i) ^n

Since we are to find for n, let us rewrite this equation:

(1 + i) ^n = F / P

Taking the log of both sides:

n log (1 + i) = log (F / P)

n = log (F / P) / log (1 + i)

Substituting the given values:

n = log (2,340 / 1,800) / log (1 + 0.05)

n = log (1.3) / log (1.05)

n = 5.38

Hence it will take Joe around 5.38 years