Question

part of the income a machine generates is put into a fund to finance the purchase of a new machine. if $1,500 is invested annually at 7% interest (compound) how many years before the fund becomes $25,000?

Answer 1

To determine the number of years it will take for an annual investment of $1,500 to reach a future value of $25,000 with a 7% interest rate, one needs to use the future value formula for an annuity and solve for the number of years.

Step-by-step explanation:

The student is asking how many years it would take for an annual investment of $1,500 to grow to $25,000 when compounded annually at a rate of 7% interest. The formula for the future value FV of an annuity (a series of equal annual payments) is given by:

FV = P × { [((1 + r)^n - 1) / r] }

where:

- P is the annual payment ($1,500)

- r is the annual interest rate (7% or 0.07)

- n is the number of years

- FV is the future value ($25,000)

To find the number of years, n, we must solve the formula for n given the known values of P, r, and FV. This involves using logarithms after rearranging the equation. As the formula for an annuity does not directly solve for the number of years, a financial calculator or spreadsheet software is typically used to find the precise number of years required for the investment to reach $25,000.