Question

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)

Answer 1

Answer:

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