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.
How long, to the nearest year, will it take an investment in Germany(4.3%) to triple its value if the interest is compounded every three months?

I got 35 years but its wrong, don't know why.

thanks

Answer 1

Pt = Po*(1+r)^n.

r=(4.3%/4) / 100% = 0.01075= Quarterly % rate expressed as a decimal.

n = The # of compounding periods.

Pt = Po*(1.01075)^n = 3Po.
(1.01075)^n = 3Po/Po = 3.0.
n*Log(1.01075) = log3.
n = Log3 / Log(1.01075) = 102.74 Comp.
periods.

102.74Comp. / 4Comp/yr=25.7 yrs.=26 yrs