The value of an investment increased by 10 percent during the first ye

As with most problems from the topic of Percentages, this problem can also be solved in a myriad of ways.
However, as usual, the simplest and the fastest method would be to assume smart values and apply the percentages on them.

Since there are three percentage changes happening, none of them being a substantially large one, it is better to assume bigger values to start off with.
I’d assume 1000 as the original value of the investment.

With a 10% increase, 1000 becomes 1100 (10% of 1000 = 100) at the end of the first year.

With a 5 percent increase, 1100 becomes 1155 (10% of 1100 = 110 and hence 5% of 1100 = 55), at the end of the second year.

With a 10% decrease, 1155 becomes 1039.5 (10% of 1155 = 115.5) at the end of the third year.

Therefore, the current value of the investment = 1039.5

1039.5 as a percentage of 1000 = \(\frac{1039.5}{1000}\) * 100 = 103.95%.

The correct answer option is B.

An alternative approach would be to use the concept of successive percentage change.

If there are two consecutive (or successive) changes of a% and b% respectively, then,

Effective percentage change = (a + b + \(\frac{ab}{100}\)) %.

In our case, there are 3 successive percentage changes. So, the effective percentage change due to these changes will have to be worked out in two stages.

Stage 1 – Calculate effective percentage change due to the first two successive changes

Since both the changes are positive changes, a and b are positive i.e. a = 10 and b = 5.
Effective percentage change = ( 10 + 5 + \(\frac{50}{100}\)) = 15.5 %

Stage 2 – Calculate effective percentage change due to the 15.5% increase and 10% decrease.

Since one of the changes is positive and the other is negative, a = 15.5 and b = -10.
Effective percentage change = ( 15.5 – 10 -\(\frac{155}{100}\)) = (5.5 – 1.55) = 3.95 %.

So, the current value should be 103.95% of the original value.

Hope this helps!