A dollar invested today grows to $1.10 in six months. What is the effective annual rate if you deposit your money in a bank for one year? please explain details.
| A. |
21% |
|
| B. |
5% |
|
| C. |
None of the answers are correct |
|
| D. |
10% |
|
| E. |
20% |
The right answer of the question is A. 21%.
The reason behind the asnwer is the concept of compounding.Compounding can be annual, half-yearly, quarterly and even monthly. Interest on compounding builds on the accumulated interest earned. In short, we are able to earn interest on interest. So, when the dollar invested grows to $1.10 in six months that means at the end of the year we are going to earn further interest of 10% on $1.10 and not $1. Here the interest rate is 10% half yearly.
Formula to calculate FV is, FV = PV * (1+i)^n where, PV is the present value of today's investment, i is the nominal interest rate and n is the compouding frequency.
FV = 1 * (1+0.10)^2 = 1.21
Therefore, the effective interest rate earned after the end of one year is 21% on the investment of $1.
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