Question

If Rachel invests $1700 today in an account that pays 6 percent interest compounded annually, how long will it take for her to accumulate $6,500 in her account?

Answer 1

23.02 years

Step-by-step explanation:

The expression that describes the future value of an investment (P) at an annual rate (r) for a period of n years, compounded annualy is:

`FV = P*(1+r)^n`

If Rachel wants to accumulate $6,500 with an investment of $1,700 at 6% per year, the length of her investment, in years, must be:

`6,500 = 1,700*(1+0.06)^n\\1.06^n = 3.8235\\n=(log(3.8235))/(log(1.06))\\n=23.02\ years`

It will take Rachel roughly 23.02 years to accumulate $6,500.