Question

A man earns $112 interest in one year on an investment of $1,400. What was his rate of interest?
8%
10%
12%

Answer 1

Here's the formula you need:
log(1 + rate) = {log(total) -log(Principal)} ÷ Years
log(1 + rate) = log(1,512.00) -log(1,400.00) / 1
log(1 + rate) = (3.1795517912 -3.1492191127) / 1
log(1 + rate) = 0.0303326785 / 1
log(1 + rate) = 0.0303326785
If log (1 + rate) = 0.0303326785
then
10^0.0303326785 = 1 + rate
1+ rate = 1.0723404255
Therefore rate = .0723404255
or .0723404255*100
7.23404255%

Answer 2

1400 -------------100%
112 -------------- x%
----------------------

x = 112*100/1400 = 112/14 = 8%

8% was his rate of interest

Answer 3

Yes it seems I made a mistake in calculating the log of 1,400:
log(1 + rate) = (3.1795517912 -3.146128) / 1
log(1 + rate) = 0.0334237555 / 1
log(1 + rate) = 0.0334237555
If log (1 + rate) = 0.0334237555
then
10^0.0334237555 = 1 + rate
1+ rate = 1.08
Therefore rate = .08 or
8%