2. You plan to invest in securities that pay 8.0%, compounded annually. If you invest $5,000 today, how many years will it take for your investment to double? 3. Using the information in the problem above; How many years will it take if monthly compounding, assuming everything else is the same? (Round to tenth decimal)

Instructions are listed below.

Explanation:

Giving the following information:

1) You plan to invest in securities that pay 8.0%, compounded annually. You invest $5,000 today.

We need to double it. Final value = 16,000. Number if years=?

FV = PV * (1+i) ^n

Isolating n:

n=[ln (FV/PV) ]/ln (1+r)

n = ln (16000/8000) / ln (1+0.08)

n = 9 years.

2) Now, the interest is compounded monthly.

Effective rate = 0.08/12 = 0.0067

n=[ln (Ct/PV) ]/ln (1+r)

n = ln (16000/8000) / ln (1+0.0067)

n = 103 months = 8.65 years