Question

This exercise is based on the following table, which lists interest rates on long-term investments (based on 10-year government bonds) in several countries in 2008.
Assuming that you invest $9,000 in the United States (3.9%), how long (to the nearest year) must you wait before your investment is worth $19,000 if the interest is compounded annually?

I got 19 years, its wrong.

Thank you

Answer 1

Pt = Po(1+r)^n.

r = 3.9% / 100% = 0.039 = APR expressed as a decimal.

n = The # of compounding periods.

Pt = 9000(1.039)^n = 19,000.
(1.039)^n = 19000 / 9000 = 2.11111.
Take Log of both sides:
n*Log(1.039) = Log(2.11111).
N = Log(2.11111) / Log(1.039) = 19.53
yrs = 20 yrs.